In order to join Golan Technologies, you'll need to undergo the following steps, both in the Darkness-client ( i.e. the Combine website ) and the Kingdom of Elysia holosite/forums.

Step 1:  Join the Combine
Join the Star Wars Combine, if you haven't already.

Step 2:  New Characters: Starting Location
If you do not have a character, or have not selected a starting location yet, refrain from selecting a starting location until you've been accepted. If you've already selected a starting location, disregard this step and continue with the next step.

Step 3:  Joining the Faction
In the Darkness client, go to the Faction section. Once there, there should be a "Join Faction" option; select that, and it will display a list of factions to join. Select Golan Technologies, and continue on to send in an application!  It is recommended that you list a number of things in the message you send with your application. Your top 5 skills, a short reason why you wish to join, and past experiences are expected in this message.

Step 4:  Once accepted
Once you're accepted in the Darkness client, you're officially part of Golan Technologies; but you're not there yet. Next step is to sign up for the Academy at the forums; follow the instructions here.  If you are an experienced player and wish to attempt to pass the Academy by examination, indicate so at that time.