Make sure the dryer's lint screen is clean. If you allow lint to collect in your dryer, it eventually blocks airflow and could cause the dryer to overheat or even catch fire. If the screen is clean, lift it out and check that the vent underneath is free of lint and debris.
Pull the dryer away from the wall and check the vent hose. Make sure the hose has not detached from the wall or the dryer. Check for any holes or tears in the hose. If the hose is bent, straighten it and put the dryer back in a way that it won't cause the tube to bend again. Check the external end of your dryer hose. It is most likely located outside of the house. Make sure it is free of lint, debris and any other obstructions such as bushes.
Make sure the dryer is plugged into an outlet. Open your breaker box and make sure no circuit breakers are off.
Open the back of your dryer by unscrewing any screws holding the back panel on. Visually inspect the wires for burns, cracks or other deterioration or damage.
Use a multimeter to check for electrical continuity. It is important to check several places along the wiring for continuity, since anywhere the electricity is not running is going to cause your dryer to stop working.
Replace the thermal fuse. Once this fuse blows, it cannot be reset. Write down the make and model of your dryer and take the information to your local appliance or hardware store to see if they have a replacement.