The short answer is that it would have to be impossibly big, and would basically take forever. The real answer is a bit more interesting.
So, while we commonly think of black holes as giant space vacuums, their pull just from having massive amounts of gravity (Thanks Quora). If there was a black hole the size of the sun in the center of our solar system instead of the sun we wouldn't even notice (except for freezing to death). Even if we were close enough to have our orbit affected by the black hole, this NASA article states there would only be a 1% chance of us actually being entirely consumed by it (although if we got close enough it would tear us to shreds and fling us into space).
The most likely chance of us being consumed by a black hole is in about 4 billion years when our galaxy collides with the Andromeda galaxy. The interactions between all the star systems could lead to us being flung off our orbit toward a black hole. If we were able to survive that it'd be just another short billion years give or take a few until the sun dies out.
So that gives us about 4 billion years to jump ship. I think given 4 billion years we could have the technology if we don't all die from destroying earth first. So, on that happy thought... Hope this helps!
P.S. I got most of my info from this video, so if you want to learn more you could follow the link. And if you wanted to learn even more you could use that video as a jump off point into the black hole of YouTube.