There are some things you can check, but you need to be willing to open some things up, take some wires loose, and do a little diagnosing.
For starters, find the manufacturer name and model number. NOTE: you didn't provide those for us, or else we would be further along with suggestions. ALWAYS have the make and model number on hand when asking anyone questions about an appliance, what might be wrong, and how to fix it.
Once you have the model number, you should be able to look up useful information from parts suppliers and often from the manufacturer itself. A wiring diagram would be pretty helpful.
1) Unplug the machine from the outlet. It is completely dead when unplugged so you don't need to worry about it hurting you after that.
2) Check the wiring diagram for the word "fuse," "fusible link," "thermostat" and "limit switch." If you can get hold of a simple multimeter, you can check these very easily.
Fuses should show ZERO OHMS, no resistance. If a fuse comes up "OL" (Over Limit) it's probably burned out. Replace it.
Thermostats, depending on where they are in the circuit, will be either closed or open - a "closed" switch is behaving as if it were another piece of the wire, and so the circuit is closed. An "open" one opens the circuit, breaking the flow of electricity. I don't mean like a thermostat on the wall in your house, controlling the air conditioner. They look a bit like very thick, oversized watch batteries with triangular ears on them, and a couple of spade lugs for attaching wires. At room temperature you can expect most of the thermostats you encounter to be closed. Look up the thermostat's model number to determine whether that is the case. If it is described in the listing as NO or Normally Open, then it should be open - "OL" in OHMS - at room temperature. NC or Normally Closed would be 0 OHMS.
Limit switches often look like the thermostats, but they're a kind of safety switch. If things get too hot, they open and some are designed to stay open until you push the plunger to reset them. Look for something like the little thermostats, but with a button on it. Press the button. If it doesn't move, it's fine. If it goes in and stays in, it needed to be reset.
NOTE: I don't often encounter limit switches of that type on dryers. It's more a thing with heating and air equipment. I'm just including it here for the sake of completeness.
Finally, check the resistance of the heating coils themselves. If you know what the coils look like inside a hair dryer, then you should be able to puzzle this out, too. Figure out where the various wire ends are - there's probably two coils in there, one bigger than the other. By running one, the other, or both, the makers can provide three different levels of heating. You'll need to find the near and far end of the coil, and put your multimeter's leads on those and check for resistance.
In a heating element, even though it isn't an unbroken wire resistance is NOT ZERO. The manufacturer's Customer Support page should be able to tell you what the resistance should be. But you know this much: if the resistance is "OL" then the heating element is broken. NOTE: be sure you're actually hooked up to the two ends of the same heating element, because being on opposite ends of two elements will also give you "OL."
NOTE: If this is a newish GE dryer in which the heating element is a large crescent moon affair right at the back of the drum, then I suspect a burned out element, especially if you tried to dry a pair of shoes. I had several of those at the facility I maintain, and users tried to dry shoes, which would bump that back plate, causing it to very briefly flex and touch the elements - ZAP - end of element. It only takes a fraction of a second and those elements burn right out. Terrible design.
I check back on my answers from time to time, if you have more questions then update your question, or comment on my answer, I will help if I can.