Summary
After being struck by a move that causes a Hard Knock-Down or a Soft Knock-Down, hold the controller Toward or Back to roll in that direction. When struck by a move that causes a Forced Tech Roll, you cannot perform a roll at all.
Re-Positioning Yourself
First things first: Rolling in Marvel Vs. Capcom 3 will not allow you to escape any combos. This is stated right away because, in MvC2, Rolling was a technique that allowed you to avoid combos that could hit you after you became grounded. In this game, Rolling is simply a means by which to re-position yourself when you get up off the ground. Rolling will never lessen the amount of time you are lying on the floor.
If you do not hold any directions after getting knocked down, your character, when they get back on their feet, will perform what is referred to as a "Tech Roll" after a similar move from previous Street Fighter games like Capcom Vs. SNK 2. The character rolls backwards a very short distance and immediately gets up onto their feet.
When you hold a direction, however, your character will roll a much longer distance in the direction you hold the controller and get up on their feet at the end of this roll. You are completely invulnerable during this roll, so there is no way the opponent can hit you out of it. The roll is, however, a fixed distance: there is no way to alter the distance your character travels.
Strategy Corner
HOW TO PUNISH ROLLS AND WHY YOU MIGHT NOT ROLL
Rolling With the Homies
One very important aspect about Rolling is that, during the roll, you are actually free to perform Cross-Over Assists! That means, right when you start to roll, you can press the Assist Button and, even before you finish rolling, your Assist, depending on how fast they are, can have already come out and started attacking. This is particularly useful if you choose to roll through your opponent and rise up on their other side. Your Assist will be called on the original side and you'll get up on the other, essentially sandwiching your opponent between you and your Assist.