What is it called when they take the male out of the male sperm to inject into the woman?

If the man gave the semen sample by masturbating, it's called IUI.

If the sperm was removed surgically, that removal procedure is called MESA. Then a sperm is injected through an egg removed in an egg retrieval via a process called ICSI, and the fertilized embryo is put into the woman. That process as a whole is called IVF, but IVF doesn't always include ICSI.