The fastest way to unclog a toilet is by plunging it. After that, you can try a drain snake, but if that doesn't work, you'll probably have to wait, either for the clog to dissolve a bit or for the plumber to arrive. Hopefully the plunger does the job.
Start with a flanged plunger with a soft rubber bell. These have a sleeve that extends below the dome part of the bell to help seal around the hole in the toilet bowl. Accordion-type plungers usually have flanges for the same reason and are just as effective. Regular cup-type plungers are ok but tend not to seal well in toilets.
Make sure the water is high enough to cover the cup of the plunger. While holding the plunger firmly, cover the hole completely with the plunger. Pump the plunger quickly about ten to fifteen times, maintaining the seal throughout the process. The idea is to create suction that pushes water back and forth in the toilet trap. After plunging, try to flush. If the toilet is still clogged, repeat this process for a few more minutes using the plunger.
If the clog is still there, try using a closet auger, or toilet snake. Feed the auger into the drain until it won't go any further. Crank the handle clockwise while pushing the snake coil as far as possible into the toilet trap. Move the snake a bit to try to free or capture the blockage. As soon as you believe that you've reached the clog, pull the snake back. Have a bucket ready to catch anything that the snake brings back up out of the toilet. Repeat if necessary.
Still have a clog? Add a few squirts of dish soap (not dishwasher soap) to the bowl, then add a gallon or so of hot water. Wait 15 minutes or, preferably, longer, then flush. The soap and hot water help dissolve toilet paper. If necessary, try this again when you can wait overnight, then try to flush in the morning.