In the process you might find that ring you lost ten years ago. It is an easy fix for anyone with the most basic mechanical skills. Sometimes it can be uncoupled by hand and other times may require slip-joint pliers. In a lavatory, (hand sink) the pop-up assembly rod will catch hair. You can shine a flashlight down the drain and see that issue and usually pull it out with something like forceps.
Bathtubs, especially those with the pop-up drains are usually an easy fix if you figure out how that damn stopper screws in. There is usually a Knob on the top of the pop-up, you hold the larger part of the "stopper" with one hand and screw the knob off with the other, (It may require pliers to start) and that will reveal a screwdriver slot that will allow you to remove the stopper and get to the hair clog. If you home is older and the bathtub is drained by a lever at the overflow level, it is a bit more difficult, but a screwdriver will gain access to the working mechanism that can be pulled out and cleaned. It may be a bit tricky getting it back in, but you can do it. You just have to ask yourself, "Do you feel lucky? Well, do you punk?"
I was a career plumber and I can tell you that I have seen more damage from chemical solutions to stopped drains than benefits from the chemicals. Usually when stopped drains become chronic it is because of a buildup of grease and soap clinging to the inside of the pipes. A strong acid may make a hole through the gunk and give you temporary relief or it may make it worse. The longer-term solution is to have the drain pipes mechanically cleaned. The only chemicals that I have used, that were even mildly effective was concentrated sulfuric or hydrochloric acid, which are damn dangerous to handle and may or may not produce the desired result.
What a plumber dreads is going to a house that has attempted, unsuccessfully, to clean the drain with some caustic solution. Many times the homeowner will even lie about it. He then removes a trap and gets doused with with acid. For me, that always increased the cost of the call, one way or another.
You can't keep hair out of drains, but you can prevent the more expensive problem that develops in sinks. Don't wash cooking grease down the drains...ever. Dispose of used cooking oil in the trash. If you fry something, wipe out the pan with a paper towel before you wash it. My house is 25 years old, and I have never had a kitchen sink drainage problem.
While I am handing out advice I will give you another free tip. When your garbage disposer starts stinking, run some cubed ice through it. The noise will wake the dead, but it will strip the metal surfaces clean and the smell will go with the buildup.