For example I want to call a 30$ bet, there are 1 25$ and 1 5$ chip on the middle, I have 1 100$ chip. I put that in the middle and want to take the remaining 70$ worth of chips back. How does this situation resolve? Does the dealer have broken chips on his stack somewhere?
Casinos use what's called the "one chip" rule: If a player pushes out a single oversized chip without verbally declaring a raise, it is assumed that the player just wants to call, and the dealer will make change. Note that this is not a choice, it is enforced: even if you push the chip then say "raise", the dealer will probably disallow the raise. If you want to raise you must either verbally declare it before you move chips, or throw out more than one chip.
Don't worry about it. It's not your job to worry about change and breaking chips. The dealer will handle this, and you will get your change back. Just make it clear it's a call and not a raise. In fact trying to do this for the dealer is a pet peeve of many dealers and it doesn't actually help them. A good general rule to have in your mind is never ever touch the pot until a dealer has pushed it over to you. The only one who should be touching the chips in a pot during a hand is the dealer to make change, rake, etc.
One thing you can do as a player is ask another player for change and get them to break your larger chip for you.