I've checked the breakers. Now I want to check the heating coil with an ohms meter. What's the best way to do this?

First you unplug the dryer and access the housing where the heater is located. Then you disconnect one of the two wires going the heating element. Set your meter for it's lowest resistance scale and check from one terminal to the other. You should have a resistance reading, but your meter should not read "OL". If your meter has a tone setting, use it. The meter should beep across the heater terminals. If it doesn't, your heater is open (and bad). If it does, then check from one heater terminal to the box the heater is in; in this position you should hear no beep nor get a resistance reading. If you do, the heater is shorted (and bad). Otherwise, you could remove the heater from the housing and visually inspect it for breaks in the conductor and also look for broken ceramic insulators that the heater coil runs through. Please repost if you have further questions.