How do you create one avatar (for a contest, for example) and display it while still keeping your "regular" avatar on the page as well?

To do that you have to save the avatar as an "outfit." With your contest avatar created in the wardrobe, click the "Outfits" tab, when click "Create Outfit." This will will save the current avatar and it will appear in the list of outfits. Click the outfit you want to share and there will be a link in a box labelled "Share Outfit on Forums". The link will look like {outfit=1234} only with square brackets instead of curly ones and a unique set of numbers representing your avatar. Copy that text and post it, and your avatar will appear!

Thank you very much. I am copying this and saving it!