Ok, so every fabulous girl is entitled to a little slip up now and then!  It can happen, and if it hasn't yet…it might.  The most common reason for things exploding is forgetting about it in the oven (never a good thing!).  This is why they invented timers!  Make sure you always, always, always set a timer when you are baking something!  You never know when you are going to forget it, then poof, you'll need this article badly!  We are not going to just deal with exploding.  What about drippings and hard crusted stuff you have no idea where it came from?  Yes, your oven has feelings and you should keep it just as nice and clean as your frig (your frig is clean right? I feel another blog coming on!).  Now I'm going to tell you something very important!  This task requires certain tools and attire.  The most important being RUBBER GLOVES.  If you don't have a pair, go to the store now!  Put the computer down and continue when you have gloves in the house!  These will save your pretty little fingers and manicures!  Don't do any cleaning without them! (no one wants yucky, dry, cracked, wicked witchy hands do they?)  I like cute ones like these!  I found them on Solutions 

To start. . . if  something "exploded" in your oven, the most important thing to do is turn the oven off immediately and (with a hot mitt) pick all of the pieces off the oven walls.  If you let these sit there, they will turn into food cement!   If we're dealing with exploding food, it's most likely a potato.  To cook a potato in the oven, you must poke some holes in it with a fork before placing it in the oven.  You need somewhere for the steam to escape.  I'm sure a lot of people have learned this the hard way.
Now for cleaning, if you have a self cleaning oven, you are in luck!  You may save a little elbow grease.  But beware! "Self Cleaning" does not mean turn a little dial and watch as your oven transforms back to being brand new!  Some require you spray a cleaner on first and some simply don't work very well. . . (sorry oven companies!)  The idea of "self cleaning" is actually to just raise the temperature so high, everything leftover just burns up.  Now this can be one big stinky mess, if you have a older model.
If your oven is not too bad but has some bad spots, an oven surface cleaner should do the trick.  Before attempting this, make sure you have your gloves and an apron on!
The best natural way is to use baking soda.  Yup, something you probably have in your pantry already!  Cover the bottom of your oven with about 1/4 of an inch of baking soda.  Spray some water on it to make it damp, not soaked.  Let sit for a few hours.  Continue to spray with water if it gets dry.  After a few hours scoop out all the now dirty baking soda.  Then you will have to take a wet sponge and clean out all the "white chalk" left behind.  Ok, here is my actual oven covered in baking soda! : )
 

Ok, my oven looks a little like a monster in this picture : )
There are also some "green" cleaners I like too: Mrs. Meyers Surface Scrub, one of the best.  (in fact, I love that whole line!)