On the LPGA Tour, about 5 tournaments each season are expected to end up in a tie after 72 holes, requiring a playoff to determine a winner. With the exception of two majors, the LPGA Tour's playoff format is a classic, sudden-death format.
Players in the playoff keep competing one hole at a time, trying to make the lowest score possible. The draw for the playoff is a random number draw out of a hat.
Any ties for the best score mean another hole for those players, and any playoff competitors that don't tie the low score are eliminated and lock up a share of second-place money. Once there is a hole where one player scores lower for that hole than any of the other remaining players, that low player is declared champion.
Some tournaments have more thrilling playoffs than others. In part, that's because some tournaments choose to vary the playoff holes while others tend to play the same hole over and over again, making a lengthy playoff boring.
However, at most LPGA Tour-run stroke-play events, the 18th hole is the playoff hole that is played over and over again until a winner is decided.