Using a snake on drains is what most people think of for this type of problem. Snakes are made of coiled spring steel the allows them to twist and turn through a drain line. They have an end on them the will give the clog a good jab. Electric snakes range in size from a small drill mounted unit to very large main sewer line snakes.
Size matters with snakes. A twenty five foot snake that works for you bathroom sink will be woefully deficient for a main sewer line. Distance is an issue. How far is your drain from the main sewer line. You need a long enough snake to reach that distance.
Another big problem with a snake are traps. Look below your sink. Do you see the "P" or "J" shaped piece of pipe? That is there to keep sewer gases from getting into the home. The trap always has water in it to stop the gases.
A floor drain, shower drain and bathtub drains all have traps that are hidden from view. Using a snake on drains with traps is harder. Hard, not impossible. Be aware that the resistance you get a few feet in is likely the trap and not the clog. Unless of course the clog is in the trap, which is common.
The article on 'Unclogging Kitchen Sink Drains' will give you better instructions on using a small snake. For a use of a snake on a bathtub, see 'Unclogging a Bathtub Drain' for more information. That will leave us with floor drains and shower drains as likely candidates for a snake. You are likely going to need an electric snake for these drains. If you have a hand snake, try it first. Apply pressure and turn the snake to get through the trap.
WARNING!! Electric Snakes Can Be Dangerous!!! Keep Control of the Snake at All Times!!!
When you use an electric snake you have keep the unit as close to the drain as possible. Hold the snake with rubber gloves and keep it straight as it turns. Apply pressure and let it work through the trap. Do not allow the snake to form a loop, it can double back on itself and twist up. Fingers that get caught in this will not do well. They can even be broken. Not to mention it can ruin the snake.
When the clog breaks free you want to keep going with the snake. Run it back and forth through the problem spot. In addition run some water down the drain while the snake is running. This will wash the debris away and help to clean the snake. Yes, this is dirty water. Learning how to unclog a drain with a snake is a little tougher. Hopefully you have gotten through it ok.