To quickly and easily clean a dirty microwave, fill a pyrex mixing bowl (or other microwave safe bowl) with water. I use the 4 quart bowl. Add a sliced lemon if you'd like. I do this every time, because I love the smell, but it's totally not necessary for the cleaning of your microwave. Microwave on the highest setting for 10 minutes. Allow to sit for an additional 10 minutes without opening the door. You've just steam cleaned the every loving mess out of your dirty microwave!
Now, carefully remove the bowl of water and using a towel, wipe down the inside of the microwave. Easy peasy!
I'd like to note that you can soak a cotton dish towel instead of using a bowl of water to do this, but I once inadvertently used a poly blend towel which burst into flames in my microwave. Ever since then, I stick to the bowl of water method. :o)
If you have a stubborn area of gunk, use your all purpose cleaner and a brillo pad. I let my microwave get pretty darn nasty and I rarely have to pull out the all purpose cleaner on anything after I steam it clean.