Once you hit Level 10, you can go to the main building in Port Oakes to register for a Super Group (basically a Guild) which also entitles you to a Base.
I had some experience building a base in Beta, so lets start with basic layout. Your base to begin with will be only 1 room, the portal into it. As you enter you'll notice (with the correct permissions) that you can Edit or Upgrade your base. Editing allows the placement of new rooms, while Upgrading allows the purchase of overall terrain for your base.
Upgrading is important, as you upgrade the amount of certain units that can be in your base. For instance you can only start off with 1 Generator, in order to get a 2nd one you have to upgrade to a Secure base.
Everything you do in the base costs your SG from their pool of Prestige. Prestige is gained when you are in Super-Group mode, you get a little bit for every kill you make. I reccommend turning SG mode on as soon as you form your SG at level 10, as you constantly build up points as you level.
Now, on to Room layout. Deciding how to layout your base is VERY important. It may not seem so to begin with but understand this : as you build rooms onto your base, you must never lose attachment from the base portal. This means that placement of your first rooms is important, as they'll usually not be easy to move around.
I reccommend making your first rooms Defensive areas. This will become more evident later as you do base raids, but by placing the rooms next to your portal as defensive rooms, you'll have a better ability to defend yourself later on (more on that in a sec).
The basic plot is a rectangle, so I suggest you begin building in one or two directions, sticking near the wall for one side. This will allow you to optomize your space in your base... with almost unlimited points to build in beta, it was still difficult to get even 85% of your available area used. NOTE: if you mess up dont worry, if you destroy a room or item you get the points back you spent on it.
The other types of rooms you'll need are Power, Control, and Workshop. These will get you the basic functionality like Power & Control and allow you to begin processing Salvage into usable items in your Workshop. Each of these areas requires different benches/items to utilize, and as you build the rooms you'll see the max allowed for each type of room. Keep this in mind as you can upgrade to bigger rooms, but many still have the same limits as small ones, which can be used to more efficiently manage your available space.
Power rooms house Generators to generate power, Control rooms house computers for control. As you build each of these you'll see your available (green) and consumed (yellow) of each resource on bars near your toolbar.
There are a few other things you'll need to know when building a base. First off is Vaults. These are secure areas where you can store captured relics that give your entire SG a bonus. In beta you could build these and they came in various types (+dmg, +xp, -debt, +resist, etc). In final however, they must be crafted or captured.
Another type of room you have available is the Teleport chamber. This is required for base raids. In order to enable base raiding, you must place 6 Anchors in your base (one per room, can only go in certain types of rooms). Once you have the 6 Anchors, you will be able to raid other bases, and be raided in turn, so be sure you have your defenses up and running before you do this!
Raids can be scheduled to a physical time ingame, for a select duration. I never got the chance to test this in Beta, so Im not sure how it works entirely.
Another type of room is Medical. This will allow anyone in the SG to choose to respawn in the base (given a Medical room with a Resurrection device) whenever they die, regardless of location. Usually this will spit you back out into the zone you were just in (in beta typically it was at the zone entrance you just went into, not at the base portal) when you leave the base after rez'ing there.
Finally you have a variety of common rooms, typically just for decoration. We selected a huge room for our guild, and decorated it with tables, chairs, trees, fountains, etc to have a place for members to hang out and chat, and to host meetings.
Hope this guide has been helpful to getting you started on base creation, I'll add more as I get more points to build things!