There is a tool you can get at any hardware store that attaches to a hose. You shove it down into the pipe and it expands and blows the clog out. We always have 2, one large enough for our main drain, and one that fits into the kitchen/bathroom pipes.
You can also try snaking it. Snakes are about $10 at any hardware store
Try using the baking soda and vinegar hack. Put about a half cup of baking soda down the drain, follow this with at least a cup of vinegar. Let it fizz for ten minutes or so or until it stops fizzing. Follow with about a gallon of boiling water to flush all the nasties away. If it is a bathroom sink, get one of those hair remover sticks, thin plastic strip with barbs, they are cheap and last a long time. Put it down the drain as many times as it takes to not get anymore hair, then do the vinegar/baking soda/boiling water to wash away all that gunk and remaining hair that was stuck. This works for tubs, too. If it is real bad it may take more than one time. More than that and the clog may be too far down the pipes for this process to clean it out and you will need a snake or a plumber with the really long snake. Been there, done that, My clog was almost out of the house in the main drain pipe. Doing the baking soda/vinegar/boiling water, with the hair removal in the bathroom periodically will keep the drains in the house working and not clogged, it will also keep the pipes cleaner. The plumber that fixed our clogged pipe was amazed at how clean the pipe was going down to the basement from the kitchen sink was (we have an opening in the pipe you can access and used it to make sure he was going down the main drain pipe and not curling up or anything. The large pipe was spotless from my attempts to clear the clog, he even said he was going to start doing it at his house and telling some customers that are constantly plugging up their sinks! I hope this helps you, Cfo!