If I ban someone in my Facebook page, will they know that I banned them?

[Vera]

When you ban/block someone on Facebook, they're no longer able to look at your account(and you won't be able to look at his either). They'll get an 'error', saying "Sorry, this page isn't available. The link you followed may be broken, or the page may have been removed."
This way, they'll probably know you blocked them or you deleted your account, one out of two.

You can't 'secretly' block someone. It'll be pretty obvious. You could, however, keep him/her as a friend, but when you post a status, you could 'block' them from it(same counts for pictures). When posting something, like a status update, you click on the little 'bar' that, right now, probably says "Friends"(for pictures, it might be a little gear). Click on it and choose 'Custom' and where it says "Share this with", choose, for example: Friends of Friends. Then there's a bar that says "Don't share this with...", you just type his/her name in there and he/she won't be able to see the status update/picture. If I'm correct, Facebook remembers your custom 'privacy setting', so you can post future status updates without having to click on the gear etc.

I hope this helped.