I'm a little late getting to this thread, but here... see if this helps...
ok, what exactly does a tablet do and how do they work?
It's basically a small special function computer with no keyboard and a touch screen. They are really good at being portable and for web browsing and reading Email and books and things like that. They are really bad at allowing lots of typing and running specialized programs (they run their own program set (called Apps) very nicely however).
I get the impression they are for surfing the net (nevermind about games, music downloads).
The can do a lot of things. The Applications available for them are too numerous to list.
Is the advantage that you can be anywhere and pick up a close by wi-fi signal so you can look something up on the the internet?
That's one advantage. Same as a laptop except more portable.
If you buy a tablet, and are going to use it at home, do you have to add it to your computer service and pay more money, or does it just pick up the wi-fi, like netflix does?
All the tablets can latch onto any WiFi signal in range. You don't have to pay any extra from your provider for that. But Tablets can also be purchased with cellular plans built in just like a smartphone. Tablets and Smartphones are really (pretty much) the same thing except that the viewing area is larger on the tablet.
If you are out and about, does it just pick up wi-fi signals, or is there a wi-fi card included, or what?
WiFi is built into the Tablets, so they will latch onto whatever WiFi signal you happen to be in range of (and can get access to). It's all included and works pretty much seamlessly.
In other words, if you buy one, are there any other additional monthly costs?
Only if you buy a Cell Service Plan with it.