Closed Team Rules are a common rule set imposed on certain team variants (variants designed to be played as a team). The most well-known example of this is probably Iron Man in Diablo 1, and a very well-known Diablo 2 example is Sirian's Elemental Strike Team.
The concept of a closed team is that of a team of players meets every so often to play certain characters. Since Closed Team Rules are generally pretty uniform in team variants, I'll list them here. Also, these rules can work with Diablo 1, Diablo 2, and Hellfire.
A group of players each starts a brand-new character to be used in team play.
Characters in the team may not play outside of the group. They should not get ahead of the others in their group by playing ahead, so unless playing to catch up (in a solo game), only use that character in team games. If playing to catch up, first make sure it's okay to do so. Not all team variants may allow solo catch up games.
Private games are usually used for team games.
Characters may trade only within the team. Trasnferring items from one's other characters to a team character is not allowed.
Characters may quit the team at any time, though they should not expect to be able to re-join. Characters that quit the team are no longer bound by team rules.
Though most team variants consist of a group of the same variant, this is not necessarily a requirement. If you wish, you could have a team of any variants.
In large groups it's usually helpful to have someone act as Team Coordinator. This is someone who works with everyone to schedule games, keeps track of what days/times games will be (to remind the other players), and keeps track of who will not show up for a particular gaming session. In Diablo 2 mutliplayer, the Team Coordinator must be careful to let everyone know which realm the team will be playing on.
In Diablo 2, Realm characters are kept on Battle.Net servers. This can be useful in cases of people who cannot fill in a particular character slot every time. Simply make a new Battle.Net account and password¹ it. Use that account to play your team variant (or variants). If you cannot make a game one day, tell the Team Coordinator the account password and he (or she) might choose to tell someone else so that they can fill in for you on the day of your absence.
¹: Use a password that you don't use for anything else. This way the password can be shared if need be.