Do I get my contact right away?

At the place where I got mine a couple weeks ago, they give you test lens that you practice putting in and taking out, and then you just keep them in when you leave. After a week you'll come back in and see how they work for you. You should come in earlier if there are problems though, or at least give the office a call and ask about it. After they make sure everything is ok, they'll place the order for your actual contacts.