How do coins get into circulation after they are made?

Answer 1

If there is a new coin or note design, then when you pay in some coins or notes of the old design, then they are got rid of. When people pay money out of the banks, they get the new design of coin or note, and gradually the old design goes out of circulation because it is no longer used.

More specifically:The following is from the US Mint:

The United States Mint ships the coins that it produces to the Federal Reserve Banks for distribution into the economy through the banking system. The money produced by the Treasury Department (both coinage and currency) is placed into and removed out of circulation through the Federal Reserve Banks and their branches. When individuals or businesses want currency or coins to spend, they write a check, exchanging one form of money (checkbook money) for another (cash). Banks satisfy this demand with "purchases" of cash from Federal Reserve Banks. This is done with special checkbook money called a reserve balance. As this newly obtained cash is spent, it flows back into the banking system as business and individual deposits. When banks accumulate more cash than they need for day-to-day transactions, they deposit it into the bank's checking account at the local Federal Reserve Bank. Sometimes the Federal Reserve Banks need additional money to replace currency notes that are unfit for circulation or to meet expanding demand. They then place orders with the United States Mint and the Bureau of Engraving and Printing (BEP).