If I withdraw money for change in the cash register, what account do I post it to?

"Please show steps of how to set up such an account"

Add a New bank account and name it Cash On Hand or Petty Cash, if you don't already have one.

"and the steps showing how to reconcile it/the two accounts."

You Count the cash on hand; that is the value you use to Reconcile to, for cash on hand. If that isn't what you see in the accounting data, someone forgot to make entries, to leave receipts, to return change, etc.

What if you didn't use your bank account. For example, I bought coins (0.25$ for 20$) from my cash on hand account. So, at the end of the day I don't count coins for my cash on hand, I keep them on my register and I count my cash on safe that I need to deposit on my bank account. How to record that transaction?

Thank you

If you are just trading one form of cash for another then you would not need to record the transaction.