The best way is to first open all the faucets to release any pressure in the lines. If you can get to it; turn off the valve before the problem pipe you want to thaw. If the pipe has already burst, then you need to repair that section (if there was pressure then there might not be a burst situation.) Look around for signs of water leakage.
Now you want to warm the pipes--don't rush this. Open cabinets to let the house's heat get to the pipers if it is a sink that is frozen. If the frozen pipes are inside a wall or in concrete other than hiring a plumber with a pipe thawing machine (assuming you don't have plastic pipes) the only thing you can do is warm up the room and wait.
A hair dryer can also assist, if there isn't any water around the area.
When you have found and repaired the area, then to prepare for next year, either insulate the pipes better or add a thermostatically controlled pipe wrap (to keep the pipes warm in colder weather.) Also consider rerouting pipes within a heated area.
Pipes that lead out of the home can be treated the same way as water pipes, but they are often underground or otherwise inaccessible. In these instances, slowly pour hot water into the drain. Alternatively, snake a piece of rubber tubing into the pipe until it reaches the ice. Boil a kettle of water and attach the end of the tube to the spout. Steam will travel down the tube and slowly melt the ice.