That site basically covers what you need to know. Remember to keep a fair amount of tension on the tape as you wrap, otherwise it looks sloppy. I personally don't leave a little tape sticking over the ends to tuck in with the bar end cap. I taper the tape when I start (like in their second advanced tip). I think it gives a cleaner line. If you do this, your bar end cap might not fit (it'll be too loose) so just wrap electrical tape around the plug until it's tight enought to stay seated.

As you wrap around the brake levers, you can leave gaps where there's no tape and be a little sloppier, since when you fold the hoods back onto the bar, they cover this area.

It's actually quite easy to wrap bars. First time I did it, I didn't have any guidance, but I could look at a good wrap to see what it should look like. If you have another bike to compare to, see if your wrap looks like the one on that bike as you go. If not, only unwrap one side at a time, so you can compare your wrap to the previous one.