First unplug it for 5 minutes to allow it to reset.
The thermal fuse helps to prevent a dryer fire by shutting off power to the dryer if it overheats. If the dryer won't start check this fuse first. Test the thermal fuse with an ohm meter or continuity checker. This is the most common part to fail when the dryer won't start. Once the thermal fuse has blown, it has to be replaced. It can not be reset.
The start switch is on the dryer control panel. Depending on the model, either press a button or turn a dial to start the dryer. If the start switch fails the dryer won't start or make any noise. Test the switch with an ohm meter or continuity checker. If the dryer hums when the start switch is activated, or if the motor runs only while activating the start switch, the motor might be defective or something might be binding the drum preventing it from turning freely. If the dryer start switch does not have continuity when it is activated, it will need to be replaced.
The door switch is located near the dryer door and is activated when the door is closed. If the door switch fails, the dryer won't start at all. Most door switches will make an audible click when they are activated. If the door switch makes a clicking sound when activated it is probably not defective. If it doesn't make a click, it can be checked with an ohm meter or continuity checker. The door switch is relatively easy to replace and is usually not very expensive.
iFixit staff suggestion: For further information to go along with Mayer's helpful answer you can go to Dryer Stops Mid Cycle which is an iFixit troubleshooting page.