They would use metal tools like tongs to grab the heated coin blanks and position them on the die.

@@AncientAthens3D Thanks. I wish you had showed this in the animation.

You're right. It is a good idea.

Firstly, they could consider the design - If It didn't looked exactly like the other coins, it was false. Second, the material could be checked - someone experienced with metals could tell if the coin was made with the same metal as the others, like copper, bronze, silver or gold. Third, wich could maybe the most effective, was to put both falsified and original coins in a balance. If they didn't weight the same, one was probably falsified.

Using sculpting techniques. Usually the design was carved into clay or wax with all detail. Then it was cast in strong metal using the lost-wax process. So the blanks, that were heated and thus softer than the dies, were struck upon them, receiving the design.

They were usually made of metal and the design relief was created just like sculptures, for example by using the lost wax casting process.

Clipping. Coins were made of precious metal and unscrupulous people shaved a sliver from coin's edge. Practically all coins that were made from precious metal and had smooth edge were susceptible to it. Punishments from being caught were often harsh.