Most clogs that form in the “trap” (the second, U-shaped, horizontal section) are caused by foreign objects that clog the drain pipe. In this case, eventually the object will have to be physically removed. Here’s how to clean a trap yourself to clear the clog, and remove that toy car (or clump of hair, or whatever!) without calling in a professional!
First, before you start unscrewing the pipe, be sure that there is not residual drain product left in the pipe. If you used a drain product, flush with at least three gallons of water, but still be very careful with handling the pipe since there could be residual pipe cleaner. (If you experience a total blockage with drain product in the pipe, you should call a plumber.)
Next, put on rubber gloves. Then place a bucket underneath the pipe to collect water. Now you’re ready to unscrew the slip nuts on each side of the trap (or simply remove the clean-out plug if you have one). Let water drain into the bucket as shown.