Summary
To perform a Throw, hold the joystick Toward or Back and press Hard Attack to perform a Forward Throw or a Back Throw respectively. Forward Throws always put the opponent on the same side they started on and Back Throws always put the opponent behind you. You can only perform a Throw when near your opponent while both of you are on the ground.
All the same rules apply for an Air Throw with the only difference is that and your opponent must both be in the air to connect an Air Throw.
To perform a Break Away, simply hit Hard Attack while holding Toward or Back on the joystick immediately after your opponent lands a Throw or Air Throw on you to escape their Throw.
Increased Role of Throwing
Throws didn't play a very large role in MvC2. In fact, you almost never saw them because landing a Throw was such a difficult task. In Marvel Vs. Capcom 3, however, Throws have been given quite a boost in effectiveness, and you can expect to see many more Throws throughout a game.
The reason Throws have become more powerful is that they have been given heftier ranges in Marvel Vs. Capcom 3. Also, they seem to come out quicker or have decent priority. What the exact factor is is not clear just yet, but regardless Throws seem to connect a lot more than before.
Everyone's Throw and Air Throw affords them different benefits. Some Throws drop the opponent onto the ground for a Hard Knock-Down that gives you plenty of time to combo off of it. Other Throws cause the opponent to recover instantly so the direct damage off the Throw is the only reward you get. But for those characters that can combo off a Throw, the reward can be huge. Characters like Sentinel can kill an opponent with half of their life left just by landing a Throw into the corner. It's definitely worth learning your best combo off of a Throw.
No Cross Throwing
You cannot Throw or Air Throw an opponent while they are in Hit Stun or Block Stun. And you cannot ground Throw an opponent who is in the air and cannot Air Throw an opponent on the ground. You cannot Throw opponents when they are floored and you can never chain into a Throw.
Break Aways
The only way to escape a Throw is to perform a Break Away. However, the window to input a Break Away is very, very small. In fact, you probably will almost never be able to react to a Throw and escape it via a Break Away. It will almost always require anticipation or, if you're lucky, even accidental Break Aways when you meant to actually attack the opponent with the Hard Attack and get thrown right beforehand.
There are actually two levels of Break Aways. If you and your opponent hit the buttons at almost the exact same time, the Break Away will push your characters away from each other and both of you will recover from the Break Away animation at the exact same time, meaning no one has any situational advantage over the other character. In this case, it's usually pretty unclear who actually landed the Throw and who performed the Break Away since the timing of the button presses was pretty much exactly the same.
However, there is a second Break Away that happens if the one player actually presses the Hard Attack button ever so slightly after the other player. What happens here is that the person who pressed the button first definitely landed the Throw and the character who hit the button second performs the Break Away. In this case, the character performing the Break Away will actually rise up into the air very slightly and drop to the floor, which actually takes just a fraction longer to recover than the character who performed the Throw. So this time, the character performing the Break Away is actually at a slight disadvantage. While they cannot be hit during the Break Away recovery, they are not at an ever-so-slight situational disadvantage in relation to the other character.
Break Aways performed in the air, however, only have the one level where both characters essentially recover at the same time. And after a Break Away is performed in the air, both characters fall away from each other.
Special Throws
Keep in mind that all of the above rules apply to regular Throws. Many characters have Throws that are Special Moves or Hyper Combos that have all sorts of different properties that may violate some of the rules that apply to regular Throws. For example, all Special Move Throws cannot be escaped via Break Away.
Strategy Corner
Back or downback and heavy will break a throw, so if you pressed L M and H to advancing guard, and your opponent went for a throw instead, you'll break away (so long as your timing was good).