The first thing you want to check is the voltage to the dryer.
You can see how this is done on my website. The dryer I have on the my site is a maytag so it will look a little different then yours, but you still check the same wires and should get the same voltages.
I will be adding much more photo's to the site when I get time.
I have more photo's then time
From there you would want to ohm out the safty fuses in back. You do this with the dryer unplugged.
If you get to this point I can post some photo's showing you how the meter will read when they are good and how it will read when they are bad.
You should not have to spend much on a digital meter. I have seen them at radio shack for $20-$30.
They are not the best meters and you would not want one if you were going to use it daily as I do, but for the number of times you will use it around the house they will last a long time and do a good job.
Be sure to ready any papers that come with your meter.
Once you have a meter you will find it usefull for other things around the house too.
John@FreeApplianceRepair.com
www.FreeApplianceRepair.com