Zangief doesn't have much in the way of mobility—a death sentence in Marvel—and consequently has remained almost entirely overlooked throughout the games lifespan. This being said, Zangief is an incredibly underrated character. His damage output is incredible, his mix-up game is above-average in the low-tier realm, and his non-techable Piledriver can stop a LOT of stuff when it's well timed.
First row: LP, HP, A1. Second row: LK, HK, A2.
Iron Claw (close): df + hk
Dash grab: f , f
Backdrop (after Dash grab connects): hp
Jump Lariat (aironly): f + hp
Body Press (aironly): d + hp
Kuuchuu Headbutt (aironly): u + mp
Double Knee Drop (aironly): d + lk
Elbow drop: b + lp
Elbow drop (aironly): d + lp
Launcher throw: db , b + lp
As Mech Zangief
As Mech Zangief
Note that once he's turned Mech, he retains that in assist form. Which means that he's both extra vulnerable and extra unstoppable.
Gief is also unique in that he is perhaps the only character with 3 useful assists.
Ground (A) is his Lariat, which can both stop and facilitate rushdown. You'll want to cover him well because he stays onscreen for awhile. Mag, Sent, Storm, Cable, can all work from this—very versatile.
Throw (B) can work well with a rushdown character like Mag or Storm—experiment with calling 'Gief, triangle jumping, then crossing them up. You'll have to make sure not to hit them just prior to the grab because Zangief can't grab in hit or hit-stun.
Air Throw (Y) is best showcased in Murakumo's Zangief vid. Makes for stylish resets.
Gief is effectively hobbled without a Wave Dash, so he's an awful point character on his own. While you can technically dash cancel with Gief (Forward, Forward, Down, Forward, Forward), it's still not particularly effective because even after the dash input it takes an instant before he gets any forward momentum.
Sent Drones, Doom Rocks, and Captain Corridor are your best friend. They clear out chunks of screen for Zangief to advance through. Storm and Spiral Projectile assists are of interest because they work very well with Gief's Aerial Russian Slam, which is his main way of forward movement. Banishing Flats are also useful to gain some ground or pressure from just outside of close range when layered with a suitable Assist.
Bread and Butter Combos
j db+HP, LP/LK, SPD : simple, effective
d+LP, d+LP, sj. LP, LK, SPD : ditto, air version
j db+HP, d+LK, HK XX LK ARS : good damage, followed by mix-up opportunity
Lariat XX (at third hit) FAB : Buster is decent damage for the meter, could be better. DHCs are possible, but you cancel out the last hit. Even so, canceling to Hail Storm is over half life for two meters, making Gief/Storm viable.
Stuff with Assists
j db+HP, LK, HK+Assist, LK ARS, (Assist Hits), Air Throw : all kinds of stuff works in this setup Storm/Spiral Proj., Drones, Tron (tricky timing), Iron Man AA, many projectile assists, many random assists.
d LP, dLP+Projectile Assist, sjLP, sjLK, sjHP (Assist Hits), Air Throw/Relaunch/SPD on the way down... : Drones, Spiral/Storm Proj., Thanos... all work with subtle adjustments (usually as simple as the difference between calling Assist then Launcher, and Launcher then calling Assist)
Random Tricks to Maximize Gief Teams
Use THC's: Gief can combo into THC's because hit Lariat Super hits fast. It can make for great chip damage when coupled with certain characters. A low-tier example is Shuma/Iceman/Gief. It chips nicely medium vitality characters.
Safe DHC's: When designing a 'Gief team. Make sure that your two other characters can BOTH safely DHC from a whiffed FAB.
Guard Breaks: You must introduce 'Gief into your guard-break attempts. With most characters, you can guardbreak with a jumping light, let them fall into Zangief A-Type assist, then whatever you want—they're broke.
Build Meter: If you get snapped in, you can build meter with sjHK xx SPD (whiffed). Whiffed aerial SPD's can also be used to hover in the super-jump state to create a ghetto fly mode. TK Lariat x N works in a pinch.
Sneaky FAB DHCs: most instant or near-instant air supers when done directly above an opponent can be DHCed to FAB. Hard to avoid if its not seen coming, and in some cases even still.
After connected Aerial Slams, you can try to follow up with a Atomic Suplex or a TK SPD.