Summary
For most characters who have the ability to fly, the command for Flying is QCB + Special. This can be formed from the ground or in the air. In the case of M.O.D.O.K., you can enter flight normally (via QCB + Special) or enter low flight mode by just hitting Up from the ground, as M.O.D.O.K. does not possess a normal Jump.
The Good and the Bad
Flying is the ultimate form of air mobility you can have in the game. Flying allows you to move your character anywhere in the air you want, moving your character almost like the ship from a side-scrolling shoot-em-up game like Gradius, though movement during flight has a lot of momentum when you move, so it's hard to stop on a dime or immediately change directions.
Along with gaining mobility in the air, you can actually use Flying in Air Combos to extend Combos much like Double Jumps and Air Dashing. Sentinel, for example, can Launch the opponent into the air, hit with a few moves and cancel the last one into Flying, and continue the combo before the opponent recovers.
However, Flying comes with the ultimate price: you are no longer allowed to Block. So once in the air in flight, you have to dodge everything. So along with the greatest mobility comes the greatest vulnerability. M.O.D.O.K.'s, however, is the only exception to this rule. Whether initiated by jumping from the ground or initiated via the QCB + Special code, M.O.D.O.K. can actually block any time he is flying.
Also, note that if you enter flight from a super jump, you will remain in super jump state and be unable to call assists. If you enter flight from the ground, a normal jump, or a double jump, you will be in normal jump state and be able to call assists.
Ending Your Flight
Flying in Marvel Vs. Capcom 3 in general does not last particularly long. They last just around 2 to 3 seconds whereas in MvC2, they would last a decent amount of time. So you have to be quick to take advantage of Flying. Once Flying ends, you'll drop straight down as if coming down from a Straight Up Jump. You can also cancel Flying early by repeating the Flight Code of QCB + Special. Once Flying ends, you cannot reactivate Flying again until you land.
Also worth noting is that, for almost every character who can fly, pressing the Special Button in the air will cancel Flying. You'll perform the attack you normally would from the air, but flight will end the instant you press the button.
Strategy Corner
Because you can 
Flying automatically by pressing the Special Button in the air, this actually allows you to perform something very similar to Triangle Jumping with characters who can fly. Basically, if you a move on the ground into flight and quickly perform a Special Attack the first possible instant, your character will go into the air and perform their Special Attack in the air very close to the ground, creating a very quick overhead attack that must be blocked high. You can catch a lot of players crouch blocking in this instance and, when coupled with Assists that hit low, you can even create some 
situations. This technique is definitely not as quick as Triangle Jumping, but is still quick enough can to be very effective in breaking your opponent's defense when they aren't expecting it.
You can also activate Flying and attack with an Air Chain Combo from the sky and, since you don't drop while flying, opponents may get fooled into trying to 
block between some of the hits of your Air Chain Combo. Thus, if they crouch, they start getting hit and if you chain into a Special Attack in the air, you'll hit them and land so you can continue your combo from the ground easily.