Its not so hard, like the above poster said, be careful if they've never been bathed before. Use a slip knot, or sometimes I'll just loop the rope around a tying post and hold the free end; if your horse responds badly you don't want them to panic or injure themselves.
I don't usually use horse soap, it doesn't seem like it makes a difference, but if you have a white horse the purple colored soap really helps get them sparkling. I swear by a jelly scrubber like this Jelly Scrubber, Horse Grooming Supplies
, I use them all the time, they have fine nubs on one side and work great on legs without being too rough. So yeah, put on soap, scrub, rinse, and let them dry.
For the show, I usually wash the day before, then spot wash very early the morning of the show so they have time to dry before the classes. Its important to look clean and sharp, it conveys respect, makes you look experienced, and wont distract negatively from your riding. Check out the other people at the show to get ideas on how to make your horse look its best, and see what trends are popular in that type of showing.
Good luck, its not hard. Prepare to also get yourself pretty soggy in the process!