When I became interested in my boyfriend, I detached and observed for a couple of months to get a critical look at what he was about (which he noticed and he thought he had done something to offend me because I inexplicably got quiet)...and then one day I pretty much just started petting his face affectionately during conversation. And I cozied up to him and draped my legs across his lap. And I put his hair in pigtails.
He was rather confused about the sudden behavior shift, but he didn't complain because I might have stopped.
ENTJ: "Hey so yah, I want you, k?"
INTP: "Holy crap, girl attention!"
He still teases me about it.
In my last relationship, I decided I liked him but I didn't know where to find him (met him at a public event, didn't have a chance to get contact info), so I pretty much tracked him down through mutual acquaintances. I learned that he was attending another public event, coincidentally showed up, flirted heavily the entire time, and then asked him out on a date.
You call it throwing yourself at them...I call it aggressive courting.