If you are interested in expanded rules for the Martial Arts skill (as it differs from Brawl), these have been pretty much lifted from Kindred of the East, a Vampire supplement. The page numbers in question are 140-141. The additional techniques below are from the Kindred of the East Companion, pp. 131-134. I strongly recommend that you buy these products if you're playing a Vampire campaign. Good stuff.
Learning and improvement of Martial Arts (even from rank one to rank two) can not be done successfully without a master. The master can teach martial arts up to one rank lower than her own rank (thus, a sifu with Martial Arts 4 can bring her students up to rank 3, but no higher) unless she has the Instruction skill, in which case the students may be able to match her rank.
In essence, there are two basic categories under which martial arts typically fall. Arts like karate, most variations of kung-fu, and kickboxing are considered hard styles. Arts such as judo, aikido, and t'ai chi are soft styles. Hard styles concentrate more on direct attack. Soft styles are more concerned with redirection of force. Here are the basic maneuver difficulties for the two styles:
Soft Strike: 6 Kick: 7 Grapple: 5 Throw: 6
Hard Strike: 5 Kick: 6 Grapple: 6 Throw: 7
Strikes, kicks, and grapples, I trust, are obvious.
The Throw: Having successfully grappled an opponent, the martial artist may attempt to throw him to the ground. This maneuver requires a Dexterity + Martial Arts roll, with a damage pool equal to the attacker's Strength. A successful throw can also stun an opponent if it inflicts three or more Health Levels of damage. Stunned characters suffer a two-dice penalty to all actions for a number of turns equal to the damage taken.
For each dot after the first, a character may have one maneuver.
Counter Throw: The: martial artist uses the attacker's own momentum against him. The defender no longer needs to grapple an opponent before throwing him and instead makes an opposed roll of Dexterity + Martial Arts against the attacker's Dexterity + Brawl, Melee, or Martial Arts (whichever is currently appropriate). If the martial artist scores more successes she deflects the attack and may immediately attempt to throw the attacker.
Deflecting Block: The martial artist, concentrating entirely on defense, tries to prevent her opponent from doing any damage, and throw him off balance in the process. When blocking, the martial artist redirects the attacker's momentum and rolls Dexterity + Martial Arts (difficulty 6) against the opponent's attack roll. Each of the defender's successes subtracts one success from the attacker's roll. If the martial artist scores more success than the attacker, the attacker must roll Dexterity (difficulty 8) or fall to the ground and take his own Strength rating as damage.
Joint Lock: Having successfully grappled her opponent, a martial artist can damage or control him by applying pressure to joints or pressure points. This torsion often results in broken arms, legs and even necks. The martial artist rolls Dexterity + Martial Arts to grapple, then may immediately roll Dex + Martial arts again to inflict damage. For each success scored, the martial artist inflicts one Health Level of damage.
Mantis Strike: This open-handed blow targets an opponent's vital organs or (against undead opponents) Chi gates and vitae centers. Difficulty 7, damage Str + loss of one Chi (if Kuei-jin) or blood point (if Kindred). Against mortals, the Mantis Strike inflicts Str + 1 damage.
Withering Grasp: By making a successful Dexterity + Martial Arts roll, the martial artist may not only inflict damage on her foe, but disarm him as well. The martial artist must score at least three success to disarm the foe; with five successes, she may take the weapon for her own use.
Blow to Pressure Point: The martial artist learns to strike the pressure points and Chi meridians in the body, thus causing significant damage. Difficulty 8, damage Str + 3.
Damaging Block: The martial artist's blocks are really attacks aimed at attacking limbs. Make a normal Block roll, but if the artist scores three or more successes, she also inflicts her Strength in damage.
Dragon Tail Sweep: This spinning leg sweep can knock the martial artist's opponent to the ground. Treat this maneuver like a Throw, but the martial artist does not have to grapple with the opponent. Difficulty 8, damage (opponent's Strength).
Elbow Strike: A quick, vicious blow, usually delivered to the head at close range. Difficulty 5, damage Str + 1.
Spinning Kick: This fast, powerful kick does significant damage to opponents, and looks impressive as well. Difficulty 7, damage Str + 2.
Thunder Kick: This deadly flying drop kick is both graceful and debilitating. Difficulty 8, damage Str + 3.
Additional Hard Techniques — requires a Martial Arts score of at least 4.
Breaking Blow: Fists and feet hardened with rigourous practice, toughened by beating hot sand or water, and charged with concentration — the powerful strikes of a dedicated martial artist can break wood, brick and bone. Performing a breaking blow requires a full turn of concentration, as the martial artist aims the blow and focuses his energies. The final strike (if it hits) adds one additional level of damage for every two full successes scored on the attack roil. (For example, the player of a character who achieved two successes on an attack roll would roll Strength +2 dice of damage instead of Strength +1.) The player should roll to strike even against inanimate objects, simply to determine the level of additional success. This is still bashing damage unless the martial artist also knows the Killing Blow technique. Due to the force of the blow, though, the martial artist suffers bashing damage equal to half of the attack's damage (before absorb rolls, rounded down). Thus, if the martial artist inflicts five levels of damage upon the opponent, he suffers two levels of bashing damage himself, though this damage may be absorbed normally by both parties Botching a breaking blow generally results in the martial artist crippling or breaking his own striking limb; the martial artist suffers a level of lethal damage.
Ground Fighting: Exotic styles like Penjak Silat stress the need to fight effectively in any terrain, under any conditions. Instead of flailing about aimlessly, a skilled fighter can use prone combat to her advantage. Skill in ground fighting allows a martial artist to attack and defend normally while crouching or prone; she suffers no penalties. Of course, the character must still be able to reach her targets.
Jump Kick: Leaping into the air, usually with a great cry or even a running leap, the martial artist plants a devastating kick upon the opponent. Such blows have enough force to crack skulls, crush ribs and destroy organs, all while carrying the martial artist across the room. A jump kick inflicts bashing kicking damage plus two dice. However, the difficulty to block, dodge or otherwise counter such a maneuver is reduced by two.
Killing Blows: A study of anatomy and a careful use of chambering and force allows the skilled martial artist to inflict devastating injury on his opponents, possibly killing them with single blows. Killing blows inflict lethal damage. No special roll or expenditure is required; the martial artist may simply decide to score lethal damage instead of bashing damage with his attacks - Killing blows may not be effective against non-human opponents, at the Mastermind's discretion. (After all, where are the vital spots on a bakemono?).
Ripping Strike: Used primarily with the Tiger Claw and Eagle Claw techniques, a ripping strike rakes across the victim with stiffened fingers bent into a claw-like grasp. The martial artist may strike with the palm of his hand, or even rip into the opponent's flesh. A ripping strike inflicts normal damage. However, such attacks are quite painful if executed successfully, and thus, cause the opponent to lose one from her dice pools for the remainder of the turn and in the following turn due to the pain - At the Mastermind's discretion, a properly executed ripping strike of significant damage (five or more health levels) may actually tear out ears, eyes or chunks of skin.
Additional Soft Techniques — requires a Martial Arts score of at least 4.
Acrobatic Dodge: Leaps, gyrations and flips allow a fast martial artist to evade many blows. Back flips and elegant jumps are the hallmarks of such stylists, and they deftly avoid the strikes of many opponents. By jumping, flipping, bending and spinning, an acrobatic martial artist may evade many blows at once. The martial artist uses Dex + Dodge as normal, but may dodge a number of hand-to-hand or melee attacks equal to his Acrobatics rating while using his full Dodge pool for each (as if evading). Executing an acrobatic dodge requires the entire turn - a martial artist cannot split his dice pool or perform an acrobatic dodge in conjunction with powers such as Rage or Hyper-Speed.
Cataleptic Grapple: With a proper locking hold, a grappling martial artist can apply pressure to blood vessels, the diaphragm, lungs, or simply against specific pressure points. In any case, the results are similar - the victim lapses into unconsciousness. A cataleptic grapple requires a successful grapple first; the martial artist must have a secure hold on the opponent. Then the martial artist must roll Perception + Martial Arts (difficulty 7); this is an extended roll, with each success inflicting one level of unabsorable bashing damage. As long as the martial artist keeps the hold, he can continue to apply pressure, stunning the opponent and even eventually killing her. As always, once the opponent is taken to the Incapacitated health level, she lapses into unconsciousness. Cataleptic grapples have no effect on Western Kindred.
Push Hands: Practice in Tai Chi includes "push hands," a game wherein the stylists press against one another in special poses while trying to force the opponent off-balance. A skilled practitioner learns to read body language, anticipate motion and shift balance with subtle pressure. When a stylist with push hands is attacked, the martial artist may defend with this technique. The player rolls a normal block, but with difficulty 7. If successful, the attacker is knocked to the ground, suffering a number of dice of bashing damage equal to his or her strength (automatic strength successes from Potence, etc. do count for this) while the Tai Chi master sidesteps and simply gives the foe a little nudge.
Reactive Strikes: Parrying, pushing and riposting in rapid succession, the martial artist seizes a brief opening to come in under the opponent's guard. When using a reactive strike, the martial artist must split his dice pool or otherwise perform at least two actions in the turn. The first action must block the opponent's attack; failure on the block negates the reactive strike. However, if the block succeeds, the martial artist immediately counterstrikes; the reactive blow can not be dodged or blocked.
Spinning Throw: By using momentum against several striking or grappling opponents at once, a master can turn a series of attackers into a mass of flying bodies. This defensive maneuver pits the weight and motion of each attacker against the others, so that they all assist in the task of flinging the aggressors away from the defending stylist. A spinning throw is a reactive throw; the martial artist must be attacked or grappled to use this ability. Effectively, the spinning throw allows the stylist to throw multiple opponents without suffering a penalty for multiple actions. The opponents must attack first, but resolution of damage is delayed until the martial artist attempts the spinning throw. The martial artist then makes one roll to throw at the usual difficulty, with a + 1 difficulty for each attacker beyond the first - difficulties exceeding 10 remain at 10, but each additional point removes a success from the final roll. The throwing player compares his successes with the attacks of the aggressors; if an attacker scores more successes, his attack inflicts regular results, while in case of a tie, the attacker fails in his strike, but is not thrown. For example, if five foolish Kin-jin attack Hideo, he can declare that he is attempting a spinning throw, and then wait for the Cainites to attack. He rolls to throw once, at a difficulty of 6 (soft style) +4 (for the first four Cainites) and losing one success from the roll (for the last Kin-jin). Hideo's player rolls and scores four successes; one is removed for the extra attacker, leaving him with three successes. Any attacker with only two successes to strike is thrown; those with three successes fail to hit; those with four or more strike Hideo normally.