I will tell you the Plumber's Secret. This is the secret that pays many a plumber's boat payment, so you must swear to respect the sanctity of this knowledge and immediately tell it to anyone in need.
You need Dawn dish detergent. No other kind will do. You will pour a half cup to a cup, depending on how bad your drain is clogged, into the drain. You will then go away and NOT MESS WITH IT for like half an hour. You will then prepare a quantity of boiling water and CAREFULLY and SLOWLY pour it into the drain. Run more hot tap water through, to judge the free-flowingness of the flow. If you are not satisfied, repeat.
Why does this work? Dawn is the grease dissolver par excellence. It will emulsify the grease, enabling the water to carry it away. Do this regularly when you begin to suspect that maybe the drain is starting to get slow.
If it doesn't work, you have a physical clog. This is most common in bathroom drains. For this you buy a drain snake and use it to clear the clog. Or you can do the easy but disgusting thing. Get something called a Zip-It. It's a long plastic thingie with barbed sides. They are so cheap they usually come two to a package. Shove that sucker down the drain, move it all about like you're doing the hokey pokey, then pull it back up. It will probably have what looks like a wet dead rat on it, which is the clog of hair that was in your drain. I think the real reason they give you two in the package is because some people just scream, gag, retch, and throw the whole thing in the tash. You won't do that, though, on account of you care about the environment. You'll clean off the clog and wash the zip-it using the newly unclogged drain.
If that still doesn't work, you may have Roots. As in tree roots, sneaking their way into your drain pipe to suck up the delicious sewage, I mean fertilized water. Once this happened to me, so I called the city. They came and snaked it from the street back to where my line branched off, and glory be the roots were in the city side. So they dug up the line and replaced it. Another time the roots were in the yard, and the digging onus was on poor little old me.
Somewhere in this magnificent panoply of secret information is the solution to your problem. Good luck, Grasshopper. I believe in you. You can do the thing.