Starting at the bar end:
I hate when the bar end tape starts getting loose. Grrr.
Here's how I start the taping: I use a narrow strip of gorilla tape to secure the end of the tape to the bar end. It's half on the bar, half for folding over inside the plug. This is way more secure than using electrical tape.
The tape end is on the bottom of the bar.
One full revolution around the bar end, no angling yet. Now I start angling up the bar, overlapping about 1/3 of the tape. Pull it pretty tight here.
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I like tapes without the adhesive strips -- silicone grippers are way easier. I often have to redo the part past the shifters to get good coverage at the turn -- lots of overlap there, and still reach the middle of the bar area.
Tapes are shorter than they used to be!