Shower Water Is Backwards, How Can I Fix It Myself?

If you mean the handle marked COLD puts out hot water and the one marked HOT puts out cold water, just reverse the handles. Usually just one screw holding them on. There may be a cap over the screw. The cap might unscrew or it might just pry off with a screw driver.

If it is a single center handle faucet, then all you should have to do is:
 
1) Remove the faucet handle;
 
2) Rotate the stem the faucet handle was attached to 180 degrees, but no more (it turns freely around-and-around);
 
3) Put the faucet handle back on.
 
Sounds strange, but it should do the trick.
 

If you don't get your answer here, then I would ask your local parts store, where you can buy parts at.  They probably know a lot about these things.  Maybe you have a neighbor or a friend who knows a little about this too.  My suggestion is to re-do the shower and reverse them.  I would definately talk to your local store and asks what they suggest.  Usually, a Lowes, or a Home Depot.  Good luck.

Swap the handles