Stationed at one of three SEAL duty stations in Coronado, CA, Little Creek, VA, and Pearl Harbor, HI, the SEALs operate under the Special Operations Command. The teams and their training, support and command structure are made up of approximately 2,500 members organized into nine active teams and two reserve.

According to the U.S. Navy SEAL official site, SEAL teams 1,3,5,7, and 17 are based at Coronado, CA and teams 2,4,8 and 10 are based at Little Creek, VA. The official site does not mention team six’s home base which is Naval Air Station Oceana, Virginia.

SEAL Team 6 (ST6) is the top tier counter-terrorism and Special Mission Unit (SMU) and is no longer actually called Team Six. Today, the same outfit is known by its designation NSWDG, Naval Special Warfare Development Group or “DEVGRU”. Not much more is known about DevGru as this excerpt from the Seal Team Six facebook page explains:

The vast majority of information surrounding DEVGRU is highly classified and details of its activities are not commented on by either the White House or the Department of Defense.

Recently, the White House released that DevGru had carried out the operation to kill and positively identify Osama Bin Laden. This is an unusual event:

The members of Team 6 are all “black” operatives. They exist outside military protocol, engage in operations that are at the highest level of classification and often outside the boundaries of international law. To maintain plausible deniability in case they are caught, records of black operations are rarely, if ever, kept.[1]

Sources:
[1] Meet The ‘Seal Team 6′, The Bad-Asses Who Killed Osama Bin Laden –  http://www.businessinsider.com/the-team-that-killed-bin-laden-seal-team-6-2011-5