Start by placing a bucket under the trap. Loosen the coupling nuts with a pliers and pull the trap off while being careful to dump all water into the bucket. Then push the clog through with a coat hanger and flush with water. Before putting the piping back together, check the washers and nuts to see if they need to be replaced. Put the p-trap back into place and hand tighten the nuts. Over tightening nuts with a pliers will strip the threads. Turn on the water and check for leaks. Tighten the nuts slightly with a pliers until all leaks disappear.
If the clog isn’t in the p-trap, it is probably in a drain pipe. There are 3 measures you can take to fix a clog in a drain pipe before resorting to calling in a plumber: homemade vinegar cleaner, plumbing snake, and commercial drain cleaner. The vinegar cleaner is a concoction of household products. First, dump some baking soda down the drain. Then dump a couple cups of vinegar down the drain and cover the opening. The mix should react and create a fizzing effect. Lastly, pour approximately half a gallon of boiling water down the drain to help flush the clog.
The next possible fix is to break down the clog with a plumbing snake. A snake can be purchased at any local hardware store and is a good tool to have at your disposal. After breaking down a clog with a snake, wash what remains of the clog down with a combination of vinegar and boiling water.
If the clog is out of the reach of a snake, the next option is a commercial drain cleaner. Find the product that you feel suits your situation best and follow the instructions. If this doesn’t work and you know the problem is in the drain pipe, it is probably time to call a plumber. Also, if water is draining slowly in all bathrooms and the kitchen, the problem is probably is the main sewer line and will require a plumber.