A microwave consists of a Magnetron, transformers, heavy duty wire, a large capacitor and a small motor to rotate its food tray. The two latter items may not be worth the effort of sorting, and I find they are better left inside and sold as mixed metal. (If you are so inclined, you can try to drain the capacitor to sell it as aluminum, but it may not even be half a pound worth. I find i’m better off getting payed for the fluid!)
The magnetron (Click link for more info) is the copper-rich component responsible for generating the microwave energy from electricity. It can be sold at motor price along with the transformer. If you know that it is in working order, you may want to try your luck selling it on Ebay. Depending on the brand, it may fetch a pretty penny, as microwaves do need repair.
The transformer can either have the copper wire cut and pulled out of it, or can be sold at motor price. The key there is to budget and optimize your time. Contrary to what a few people might think, there are NO precious metals in a microwave… unless of course you count copper as well.
When scrapping out a microwave, always consider selling reusable parts. Things like panels, and especially the rotating glass tray, are able to fetch upwards of $20 on eBay, so long as you title everything as specifically and with as much description as possible.