The advantage of Facebook is that you can get more insight into who they are, see more photos, find out the kind of circles they hang out in.
It’s slightly stalkerish, but remember; they will get to see everything on your profile too so it’s a fair swap.
There are two main ways to transition away from whatever dating site you are using: the first way is a slower process but it’s probably the safest option, while the second is very “high risk-high reward”, but is the quickest method if done correctly.
The slower method is about building trust and rapport.
With any luck they will like you back and you can look forward to a new life of love, romance and passionate lovemaking. In reality, it’s like that game at the fun fair where you have to shoot a row of ducks but nobody ever seems to be able to hit the target.