Ok, obviously, when something like this happens...
you should clean it up right away to avoid cooking on those stains that are more tough to remove. But if you're like most of us (me), you were already hungry when you decided to nuke your meal so...yeah, you got yourself some fossilized food splatter, don't cha?
You can loosen up the stains with steam by either 1) throwing in a water-soaked sponge, put on "high" for 2 minutes, and let sit for another 5 minutes so you don't burn yourself
or 2) put in a microwaveable bowl of water with a dash of baking soda or lemon on "high" for 5 minutes. Remember to be careful and use mitts or allow the bowl to cool before removing.
The steam from either of these methods will soften the stain and help with removal.
If you've REALLY let your stains yellow the inside of your microwave (very common with burnt popcorn!), then try using acetone nail polish remover to wipe off the offending marks. Wash the area with soap and water. Allow it to air out before use.