Nobody likes it, but sometime or another, every homeowner is faced with a toilet that backs up. Consider it a rite of passage. Toilet problems are stressful because there's usually some urgency involved.
The first order of business is not to panic. Instead, become a detective and determine whether or not any foreign object may have ended up in the toilet bowl by accident. Households with young children are very prone to toilets that play host to all manner of toys. If this is the case, you may be able to put on some sturdy gloves and just fish the object out. You can also try waiting for the water in the toilet to drop to a normal level and then pour a bucket of water into the bowl. The added pressure will often dislodge blockages and send them on their way.
If that doesn't work, use a plunger to clear the toilet. Flanged plungers are best for toilet clogs because they make a better seal and increase the amount of pressure you send down into the discharge siphon tube. Accordion style plungers are effective, too. Just make sure that the suction cup is completely covered with water before you start plunging. Add water to the bowl if you have to.
Another choice for clearing clogs is to dislodge them using a plumbing snake, or closet auger, a length of coiled metal that you can thread from the toilet bowl down through the serpentine piping of the toilet to free anything trapped there. Snakes are relatively inexpensive options that are available at your home improvement outlet.
If these options don't work, most plumbing supply stores carry compressed air or carbon dioxide cartridge delivery tools that will provide stronger pressure than a standard plunger to clear clogs. They're more expensive than plungers, but are a lot less costly than hiring a plumber.
As a last resort, you can uninstall the toilet, upend it and get at the clog that way. There's definitely a gross out factor involved here, but it might be better than a large plumbing bill.
Actually, most toilets are relatively easy to disconnect. After you've unbolted the tank from the bowl, the bowl is typically attached to the floor with hold down bolts and sits on a wax collar. Once the bolts have been removed and you've removed the caulk around the base, it isn't hard to get the toilet off the collar and onto a plastic tarp for easy access.
Cushion the area under the tarp with an old blanket to avoid cracking the toilet when you set it down, and cover the drain opening to keep gas from escaping into the room. You'll also want to replace the wax collar before reinstalling the toilet. Toilet removal isn't complicated, but toilets are heavy, so make sure you have a helper.