When the DNA has been put into bacteria, they can produce large amounts of protein for us. We grow the bacteria in a "soup" made from all of the food they require. As always with bacteria and genetics, a lot of thought is given to safety.
The protein of interest has to be separated from the thousands of other proteins which the bacteria produces for its own sake. This is usually done by putting the contents of the bacteria through columns of tiny beads, to which our protein should stick differently from how the bacterial proteins do.