Executed by performing a Shoryuken motion? and pressing punch, T. Hawk ducks down and crosses his fists in front of his face, then rapidly stretches his arms out behind himself and jumps diagonally up, ramming his opponent in with his head and/or shoulder ("Tomahawk!").
The reach of the attack is determined by the punch button pressed: the heavy punch version has the longest diagonal range, while the light punch version is much more vertical, and medium punch version is the most balanced of them.
The EX Special version introduced in Super Street Fighter IV has enhanced (albeit still limited) invincibility on startup and travels upwards faster at the same angle as the medium punch version, but T. Hawk can only execute an EX Condor Dive immediately after an EX Tomahawk Buster.
In the Arcade Edition update, performing the EX Tomahawk Buster is no longer mandatory to perform the EX Condor Dive - thus making both EXs independent from each other just like any other move in the game -, but the chaining still exists as being now optional. This was likely done as a method for rebalancing T. Hawk's moveset.
This attack is a go-to anti-air for T. Hawk, and the brief invincibility on startup can be used to evade projectiles if timed correctly. It can also finish combos and punish opponent mistakes at close range.