The early stages on af MTT is pretty similar to cash games, because stacks are still deep, and chips won are almost as valuable as chips lost. The biggest difference is typically, that there is an ante, which gives you an incentive to play slightly wider ranges from all positions. But in general if you are a good cash game player, the early stage of an MTT should really not present you any problems, because at the end of the day its still poker.
The adjustment comes, when stacks get shorter, like 30-40BB or less. As a cash game player you most likely dont have much experience playing with these shorter stacks, and this is where, you need to evolve your game. You also need to learn and understand ICM, both when its very important, and when its not so important.
Some of the adjustments coming from shorter stack sizes is smaller open sizes and also smaller bet sizes postflop in many situations. Whereas people might be at least somewhat elastic in cash games, in tournaments sometimes a small C-bet like 30-40% pot can get almost as many folds as a larger C-bet, because a player starting the hand with just 21BB dont have a lot of room to call you now and make decisions later. Especially since he cant just add-on, if he lose the hand. He need to preserve his last chips, so he will often only fight back at you, if he hit the flop in a big way.
So the play become much more focused on preflop and flop, and not so much turn and river. Sometimes you can take lines like overbet jamming the turn with an overpair on a wet board, where its very likely, your opponent has some sort of draw after check-calling flop. In a cash game you would typically use a smaller size or maybe even check back for stack protection.
When you get near the bubble and especially on the final table it become really important to understand the dynamics with stack sizes. If you are a middling stack, you dont want to get involved with the players, who can bust you, while much shorter stacks are still hanging around. And if you do get involved, you want to do it in ways, where they can not outplay you. Like maybe rejamming your 21BB stack over their open raise rather than just call and face all kinds of tough decisions later.
Speculative
hands like small pairs or suited connectors go down in value, when stacks get short, while hands with high cards go up in value. With an effective stack like 20BB, you rarely want to open a hand like 44, because you are only happy, if people fold, and in that case you want to use hands with blockers like A4o instead.
And then finally you need to learn the preflop push-fold ranges. Both which hands to open shove, when stacks get shorter than 10-15BB, which hands to rejam over an open with 20-25BB, and which hands to call a shove from other players with. There is software like ICMizer for this, and its an important part of tournament poker, which you cant afford to be completely ignorant about, if you want to do well in tournaments.
