Take off the cover to the drain to give yourself better access to the piping underneath it.
Insert a metal pipe snake down the drain and continue to force it down the pipe until it stops moving forward. This is the likely location of the pipe clog. Wear rubber gloves when doing this.
Twist the pipe snake to help wedge it into the clog a bit more. This helps clear it once you turn on the snake.
Turn on the drain snake and hold onto it as it vibrates back and forth. Push the snake forward into the drain and then pull it back slightly several times to help break up the clog.
Run a towel over the snake as you pull it back out because it will likely be covered in filth. Have a bucket handy to dispose of any hair or debris that comes out of the drain with the snake.