I used to show my fleeces every year. Loved doing it.
First off, make sure your fleece is very clean, even to the point of going through it for a couple of hours. Carefull not to disturb the set of the fleece. Make sure it is well skirted, all the tags, belly, leg and neck wool removed.
Take a bit of the fleece (from the edge) in your hand and with both hands pull on the fleece. If is stays firm, it is good to go. If it crackles or breaks, it will not fair well at the shows. This means at some point your sheep were worried and has stress breaks or weakness in their fleece.
For folding, depending on size of fleece, lay cut side up, fold in half and roll. For big fleeces, fold in thirds, both ways. Place in Clear plastic bag.
I know the judges I had were very, very picky about the quality of the fleece they judged. But it can be a lot of fun. I sure miss it.
Here are a couple of web sites..
http://www.margaret-peel.com.au/skirting.htm
Here is a web site, with what I said, but said in a much better way!
http://www.frelsifarm.com/article_contest.htm