As an Argon Cadet, you will receive your Headquarters in a new mission. You will receive the mission after about 10 minutes.
Talk to Brent at the Secret Service Outpost.
Fly to the shipyard in Argon Prime Alpha.
Approach the Argon Mammoth next to the Shipyard.
Once you get close, the Mammoth will become hired, and you can then tell the captain where to go. Send it to the sector you will like, then tell them to drop it.
Remember, that you can pack it up and move it elsewhere once you have your own TL, so dont worry to much about its initial placement.
It may take awhile to fly to where you want it. Be careful about sending it through hostile space.