How do you go about playing different time controls: rapid, blitz, bullet?

Especially rapid?

It's a different mindset -- and different priorities.  Clearly, the clock becomes ever more dominant with shorter time controls, and so your priority as a player must be to properly handle the clock.  This also means that your style of play and even decisions may be influenced by the clock -- e.g., sharper, less predictable play (if you can handle it) may yield better results against people who don't defend so well, and defending well is always time consuming.  Also, you may choose very different moves in a blitz game precisely because with only a few minutes for each player it's less likely that non-obvious mistakes can be caught easily by the opponent. 

That's my perspective, but I must say that I am not the best blitz/rapid player, so other strategies and suggestions may indeed be more effective than mine.

I wrote a nice post about this very topic, feel free to check it out:

https://www.chess.com/blog/EnergeticHay/how-to-navigate-different-time-controls-classical-rapid-blitz-and-bullet

I think as the level of opponent increases, the time pressure decreases and essentially all 3 are similar. It's just that in bullet you play a lot more from memory and in rapid you play a lot more from calculations. But the memory is of previously calculating the move so the end result is the same in essence.