Try and clip the bars/front wheel to something solid so they're not flopping around and you can use both hands.
Peel off the back tape a bit at a time to save the tape from becoming stuck to itself.
Take your time, it's a job to be enjoyed (honest!)
Start at the bottom and go inside up, outside down, keep the overlap constant. When it comes to going round the STI's I've seen it done a dozen different ways. Personally I never bother with the little extra bit to stick over the clamp, I do a weird little figure of eight double wrap.
Trim any excess at a slight angle then finish off with electrical tape (which you will of course have ready cut and easy to hand!)
Bar tape is a tricky one, most people don't do it often enough to be good at it and a badly wrapped set of bars looks dreadful, especially if it starts unwrapping itself. If you're being really picky you will match the number of turns on each side of the bars – when I rebuilt my girlfriends road bike I had to undo one side of bar tape and redo it to get it to match. 😳