As it stands, martial arts in storyteller are a bit of a nonissue - they are character background only, and make no fundamental difference to the system - its still "I hit/dodge/disembowl".
A proposed alteration is to use secondary skills/talents for a martial art, and that the art allows players to select special manuevers as does Brawl in the core rules.
For example: Frank decides his character is a student of the martial art MArt. MArt's style is one of quick and adaptable moves rather than of heavy decisive blows. Frank and the ST have a chat about what sort of manuevers and such and work out something they are both happy with.
Frank decides to take 2 points in Dodge and 2 points in Brawl, in addition to his 3 points in MArt - he decides that his character learnt to punch on first, before learning MArt. He takes Evasive Action and Taunt as his brawl special manuevers.
After talking with the ST, Frank takes a maneuver they call Double Up - the character has learnt to dodge a blow with such adeptness that he can follow up a dodge with a strike. In game terms, the player declares a dodge, and if they have any spare sucesses above what was necessary, these are used to make a strike. The maneuver uses two actions, but the player can choose after sucessfully dodging to strike (ie: they know they will hit). The roll is Dex + MArt.
For instance, Frank's character (let's call him Furter) is fighting against an opponent (call him Oppy). Oppy strikes at Furter, and Furter dodges, calling on his knowledge of MArt to avoid the blow. Oppy's player rolls Dex+Brawl and gets 2 sucesses, Frank rolls Dex+MArt and gets 4. Frank chooses to strike back at Oppy as he moves out of the way, knowing Furter will hit. Frank rolls for Furter's damage.
This may be a bit bloppy - its intended to illustrate rather than to provide a firm working suggestion. Different maneuvers could be developed for a given style of art. This isn't intended to overcrowd the system, but more to provide for those folks who want to have learnt to have beat people up in a particular way. Not all of the maneuvers need to be actual combat maneuvers either.
Another example: Frank decides that MArt also would allow an observant person to get an advantage over an opponent if they see them fight. He suggests to the ST a special maneuver of that type and they work out mechanics for it.
If Furter does not take action against an opponent for a turn, but either observes or simply dodges/blocks, at the start of the next turn, Frank can roll Per+MArt at difficulty 7. For each 2 sucesses, Frank gets a -1 difficulty to dodging or attacking (using MArt) against that opponent. This benefit lasts for the scene, or if the opponent is sufficiently experienced (3 in brawl/dodge/etc) or knows multiple arts, they can realise what is happening and try and change their style, removing the lowered difficulty.
Fighting Oppy again, Furter drops back and watches closely as Oppy strikes at him. At the end of that turn (not tick, one whole turn), Frank rolls Per+MArt. He only gets 2 sucesses, giving him a -1 to strike or dodge when rolling Dex+MArt for the rest of the combat, Oppy being just a thug and not well trained.