Inquire with store where you purchased your microwave. It may participate in a take-back program where you can drop off your microwave at the store or another facility. The store might also have a trade-in program that gives some credit if you need to buy a new microwave.
Call a local recycling center. It likely accepts used microwaves.
Contact a local solid waste facility and ask if there is an area where you can drop off a used microwave. For a fee, you may also be able to arrange for them to pick it up. The facility's website may also contain this information as well.
Call a local junk removal or hauling business, which will likely pick up your used microwave for a fee.
Check with your community leader to see if there is an organized dumpster day. If so, ask if they will have a special area for small appliances or electronics, such as microwaves and computers.
Donate a working microwave to a local charity, thrift store, food kitchen or homeless shelter.