Check the power source. Most of the time, power issues can be resolved by simply resetting the circuit breaker in your fuse box.
If resetting your circuit breaker does not work, check the wall plug to see if it is working. Unplug your dryer, then plug in your washing machine or some other device into the wall slot to see if it powers on.
Check to see if the door switch is stuck in the closed position. The door switch is what activates your dryer and it can become defective or stuck.
If it is stuck, pry it open with a putty knife or a flat-head screwdriver. If that doesn't work, chances are you have a defective switch and will need to replace it.
Inspect the thermal fuse. Most dryers have a thermal fuse that protects the dryer from overheating.
Usually, this is mounted close to the exhaust duct. If your dryer's thermal fuse is blown, it will not turn on at all.
Check your owner's manual to see where it might be located and replace it.