How do I switch from one iPhone to another?

I have an iPhone 4S that I've had for a little over a year. I'm very interested in the iPhone 5, but I don't know how - exactly - to go about getting one.

I mean, if I buy a new iPhone from the Apple Store (either online or in the actual store), it will be a new phone with a new plan and number, won't it? I don't want that, I want to replace the 4S on my plan with a 5, but keep the same number. Can I do that through the Apple Store? If so, how? Or do I have to go through AT&T instead? I'm just not sure how to go about doing this.

I don't want to mess around with unlocked phones or anything like that, BTW.