In order for your Weapon Plant to build weapons, you'll need to store your weapon Jitters in it. To store your weapon jitters from the overhead view, simply drag them from your backpack onto your Weapon Plant. To stow all your weapons at once, just point at your Weapon plant and hit "F3".

To stow your weapons from 1st person mode, move into the weapon paddock, and press the "F3" key.

Double click on your Weapon Plant to expand the Weapon Plant inventory. If you look at your Weapon Plant inventory, you will see that its inventory bar is partially filled. Keep an eye on this to know when its capacity is filled.

Find the "FirmPoint" icons on your weapons (FP) and look at the different values. Your Avatar has two FirmPoints, so you can hold weapons with a rating of 1 or 2. Later, you can increase your FirmPoint Rating to 3 or even 4 with certain Armors or Modifiers. Weapons with 5 FirmPoints can only be used by Rovers, which have varied FirmPoints ratings. If you are inside your Nerve Center, you can access the Inventory pages to get more detailed information on a weapon or any other item. Select a Weapon, and choose "BUILD".

When the weapon is finished building you must enter the paddock to pick it up. Once you touch it, it will move to your Weapon Inventory.
To change weapons, hit the "C" Hot Key. This will cycle through any weapons you are carrying. If you try to equip a weapon that has too many FirmPoints, you will be given a warning.

You can also equip a weapon by opening your Weapons list, and "Dragging and Dropping" it into your weapon slot directly beneath your Avatar portrait. If you have any armor Jitters, try building an Armor Factory and then some armor, and then equip it on your Avatar in the same fashion.