Well, you need to attack the base when the base is vulnerable. The base is vulnerable for two out of the twenty four hours in the day. Then, you need people with these skills:
1) Bounty Hunter: Investigation II
2) Smuggler: Slicing I: Terminals
3) Bio Engineer: Novice Bio Engineer
4) Commando: Heavy Support Weapons I
5) Squad Leader: Novice Squad Leader
The people who have those skills need to do a certain thing to the terminal in that exact order. Once the squad leader overloads the primary terminal, you must defend the base for a certain amount of time, before it blows up. If a declared enemy of the enemy faction is able to stop the self destruct sequence, you must wait five minutes before the Squad Leader can overload the terminal again.