Speaking as someone totally clueless ... it takes some time and a LOT of patience. Be prepared to spend a couple of hours the first few times you try it, and be careful with it because you'll probably wind up unwinding and re-wrapping several times. Starting the plug end so it doesn't make a big lump is the hardest part and I still haven't got that down. Straighter bars are easier than ergo bars - the more bumps, bends and curves, the harder it will be.
There are some good online guides to wrapping bars - I want to say I used the one on the Park Tool site.
It's a useful skill to have, so I do plan to do it myself again when my current tape needs to be replaced (probably this summer), but so far it looks a lot nicer when I let the bike shop do it. If you don't have the time or patience, it shouldn't cost much - I've never paid them to do that job alone, it's only been in conjunction with replacing shifters, etc.