With so many things that can get sent down the drain it’s not a mystery on how they get clogged.   Lesser blockages you can take care of yourself actually, though at times, if none of the below methods work it might be time to call a professional to unclog your drain.   Common blockages are caused by grease, hair and food particles that make it down the drain.
A few ways to unclog a drain yourself are:
A Plunger
In the same way that you use a toilet plunger to unclog a toilet you can use it to unclog a drain in your sink or tub.   This is one of the easier and reliable ways to clear a blockage.   Just be wary of the condition of your pipes.   With a plunger you are creating a buildup of pressure in your pipes to push the blockage clear.   But if the blockage is set too firmly in place that pressure could damage the pipes themselves.   Especially if you have old copper pipes or that faulty PVC piping that tends to fail.
A Snake
For more serious problems you might need a snake to unclog drains.   A plumbing snake is a long flexible cable that is also known as an auger.  You can pick up an auger or snake at most hardware stores and they take a bit more work to use.   You either feed the snake right down the drain to push any blockage out of the way or you might have to remove the pipe under the sink to get at the clog more directly.
Chemical Solutions
The solution that will is the easiest but does little to the more serious drainage problems is either using baking soda and vinegar which can break up and unclog a drain, or a chemical drain cleaner that you can get at the grocery store.  The first solution you can let it sit overnight to eat away at the blockage.   The latter solution you should follow the directions because if you leave too long in your pipes it could cause damage to your pipes, and that’s a much bigger problem than a just unclogging your drain.
Of course, if all else fails don’t be afraid to call in a professional.   Plumbers are pretty good at unclogging drains.