We do *not* charge for our service- it's completely free from our end.
The charges that may apply are those that you would normally pay for sending/receiving text messages (or data if you're using the app).
It's charged as a normal US mobile number- so whatever you would pay to text someone, it costs the same towards the group. Each text you send to a GroupMe number counts as one text to a mobile phone number—you are not sending five messages if your group has five members.
Some people who aren't on an unlimited plan have a certain number of texts they may send and receive per month, so they should keep an eye on that count with their cell provider.
If you don't have a text message plan, we strongly encourage downloading the app if your phone allows (iPhone, Android, or Windows Phone available at http://GroupMe.com/apps).