How come when people think another person is attractive they tend to stare at that person for awhile

Human nature

For the fun of it

They stare because they are captivated by the girl/guy's beautifulness or handsomeness :D

That's a good question, I'd answer it if I had any clue why...
I guess its just what we do

If something looks particularly good, you tend to look at it.
Its also a subconscious way of broadcasting that you like them I reckon.