Crimson Viper is one of the new characters in Street Fighter IV.
She's the only character that can super jump (tap down, then up) and she can cancel her moves by super jumping as well, giving her an array of tricks and level of mobility the rest of the cast don't have.
She's also something of a combo machine but this is balanced by the fact that C.Viper struggles to get close enough to some characters to start those combos.
Thunder Knuckle (quarter-circle back + P)
C.Viper's Thunder Knuckle is one of her safer ways to approach enemies. The LP and MP version slide along the ground while the HP version catches jumping opponents (if it hits them high enough, you can combo into another HP Thunder Knuckle). The EX version is really slow but sets up a free combo if it connects.
Burning Kick (quarter-circle back + K)
This move is best done from the air, just above the opponent's head. From this area, it can be really hard to guess which way to block, which gives C.Viper that all important knockdown she needs to get close. The EX version has a lot of invincibility, so it's good as a wake-up move.
Seismic Hammer (towards, down, down/towards + P)
Her 'fireball', that sees her slam her fist into the floor and cause a shockwave elsewhere on the ground. The EX version hits the enemy high up into the air, allowing for further juggles.
Emergency Combination (quarter-circle towards, quarter-circle towards + P)
You'll be using meter on EX Burning Kick and EX Seismic Hammer but if you save up enough for a super, tag it on the end of a LP Thunder Knuckle for an easy way to land it.
Burst Time (quarter-circle towards, quarter-circle towards + PPP)
Learn how to combo into this Ultra in the corner. It takes a deceptively long time to start-up, so it's quite easy for the opponent to bait you into wasting it as they safely hide behind block. EX Seismic Hammers are the best way to set this Ultra up.
Basic Combo: cr.MK xx LP Thunder Knuckle xx Emergency Combination
Advanced Combo: (in corner) Jump in HK > HP xx EX Seismic Hammer (super jump cancel) > air Burning Kick > Burst Time