I assume it doesn't connect to anything (other than the satelite I guess), is this right? Or it does and has some kind of charge?
GPS, the Global Positioning System run by the United States Military, is free for civilian use, though the reality is that we're paying for it with tax dollars.
However, GPS on cell phones is a bit more murky. In general, it won't cost you anything to turn on the GPS in your cell phone, but when you get a location it usually involves the cell phone company in order to get it quickly with little signal, as well as get a location when the satellites aren't visible (since the gov't requires a fix even if the satellites aren't visible for emergency 911 purposes). It uses up some cellular bandwidth. This also means that for phones without a regular GPS receiver, you cannot use the GPS at all if you don't have cell phone service.
For this reason most cell phone companies have the GPS in the phone turned off except for emergency calls and for services they sell you (such as directions).
This particular kind of GPS is called assisted GPS (AGPS), and there are several levels of assistance used.
A normal GPS receiver listens to a particular frequency for radio signals. Satellites send time coded messages at this frequency. Each satellite has an atomic clock, and sends the current exact time as well.
The GPS receiver figures out which satellites it can hear, and then starts gathering those messages. The messages include time, current satellite positions, and a few other bits of information. The message stream is slow - this is to save power, and also because all the satellites transmit on the same frequency and they're easier to pick out if they go slow. Because of this, and the amount of information needed to operate well, it can take 30-60 seconds to get a location on a regular GPS.
When it knows the position and time code of at least 3 satellites, a GPS receiver can assume it's on the earth's surface and get a good reading. 4 satellites are needed if you aren't on the ground and you want altitude as well.
As you saw above, it can take a long time to get a position fix with a normal GPS. There are ways to speed this up, but unless you're carrying an atomic clock with you all the time, or leave the GPS on all the time, then there's always going to be a delay of between 5-60 seconds before you get a location.
In order to save cost, most cell phones share the GPS receiver components with the cellular components, and you can't get a fix and talk at the same time. People don't like that (especially when there's an emergency) so the lowest form of GPS does the following:
This saves a lot of money on the phone design, but it has a heavy load on cellular bandwidth, and with a lot of requests coming it requires a lot of fast servers. Still, overall it can be cheaper and faster to implement. They are reluctant, however, to release GPS based features on these phones due to this load - so you won't see turn by turn navigation here.
More recent designs include a full GPS chip. They still get data from the phone company - such as current location based on tower positioning, and current satellite locations - this provides sub 1 second fix times. This information is only needed once, and the GPS can keep track of everything after that with very little power. If the cellular network is unavailable, then they can still get a fix after awhile. If the GPS satellites aren't visible to the receiver, then they can still get a rough fix from the cellular towers.
But to completely answer your question - it's as free as the phone company lets it be, and so far they do not charge for it at all. I doubt that's going to change in the future. In the higher end phones with a full GPS receiver you may even be able to load your own software and access it, such as with mologogo on a motorola iDen phone - the J2ME development kit is free, and the phone is only $40 (prepaid phone with $5 credit). Unlimited internet is about $10 a month, so for $40 to start and $10 a month you can get an internet tracking system. (Prices circa August 2008)
It's only going to get cheaper and more full featured from here on out...
Re: Google maps and such
Yes, Google maps and all other cell phone mapping systems require a data connection of some sort at varying times during usage. When you move far enough in one direction, for instance, it'll request new tiles from its server. Your average phone doesn't have enough storage to hold a map of the US, nor the processor power to render it nicely. iPhone would be able to if you wanted to use the storage space up with maps, but given that most iPhones have a full time unlimited data plan most users would rather use that space for other things.