Super Saiyan 2 can only be achivied by someone that has reached Super Saiyan.
The person must become enraged by something (ex: when goku is killed by cell gohan turns Super Saiyan 2).
If the Saiyan trains hard enough he can reach Super Saiyan 2 but again the Saiyan must have reached Super Saiyan.
Details of Super Saiyan 2: The hair sticks up more and there are more hair strains then Super Saiyan.
The body becomes much stronger the speed is increased. The fighter become almost twice as powerful as a normal Super Saiyan.