How did the Weeping Angels in the Doctor Who episode "Blink" get the key to the TARDIS in the first place?
tl;dr: We don't know, because it happens off-screen, but it most likely came from The Doctor himself.
The key thing to understand about Blink is that entire episode is cyclical. From Sally Sparrow's perspective, the episode happens as we see it. But from the perspective of The Doctor and Martha, the end of the episode happens before the beginning.
At some point after/before the episode, The Doctor encountered some Weeping Angels in the abandoned property. The Angels wanted to use his TARDIS to feed themselves back up to full strength. The Angels managed to send The Doctor and Martha into the past. We are left making the assumption that they also stole a TARDIS key at the same time.
Unfortunately for the angels, the police department found and moved the TARDIS before the Angels could get to it. They can't exactly search through the city for it, so they were a bit stuck. Then Sally came along and took the key, as well, and the rest of the episode happen.