Minor plumbing issues can usually be resolved without the help of a plumber. A clogged toilet, even a severely clogged one, is a prime example of something you can handle yourself. All you will need is a plunger and, perhaps, a snake. If you don't have either of these tools, you can pick them up at your local home-improvement or hardware store. They're usually very inexpensive.
If neither of these methods work for you, there may be a more severe issue that's causing your drains, including the one beneath your toilet, to back up. If you suspect that something else may be wrong, call a plumbing service to help you out, but only after the following two methods have failed.
The Plunger Method
This is the go-to method for unclogging a toilet since it works the majority of the time. It's also very easy to do. Before beginning, make sure that your toilet has some water in it, but not too much. If it is filled to the brim, wait several minutes for the water to go down. If it is dry, you will have to add some water because you won't create much suction without it regardless of how vigorously you plunge.
To begin, fit the plunger over the toilet drain and give it a gentle push. The goal is to force all of the air out of the plunger and create a tight seal between the plunger and drain. Once you have created a vacuum, you can plunge using a back and forth motion. Vary the speed and force of your plunges until the clog comes free and the water drains freely down the drain.
The Snake Method
Only use the snake method if the plunger method has not worked after several attempts. Slide the snake down your drain with the coiled end going in first. Keep pushing the snake down the drain, navigating around the curves of your pipes, until you encounter the clog. Once you encounter the clog, turn the snake clockwise so that the coiled end will break up the clog. Continue until you can push the snake past the obstruction and the water flows freely down the drain.
If the snake method has not worked after several attempts, you will have to call a plumbing service or home-improvement company to take care of the clog for you. There may be something else, like a collapsed sewer pipe, that's not allowing the water to flow freely.