There is an inexpensive way to do this, actually. It's not as good as a real sleep study of course, but it works.

Go to eBay and search for "usb pulse oximeter". They're about $100. Wear it overnight (tape helps) while the software graphs your blood oxygen level.

If you have sleep apnea, at some point during the night, your oxygen will dip significantly and your pulse will spike at the same time. It is easy to see this event on the graph. Depending on how much of a dip there is, and how often it happens, determines the severity of your sleep apnea.

I have sleep apnea myself and have had a real sleep study done. I use the pulse oximeter at home to verify the effectiveness of whatever sleep apnea treatment I'm using at the time (cpap machines, different kinds of cpap masks, dental devices, etc).