You can build and expand your base by spending the materials and supplies that you collect while running. To construct new buildings, tap the green tab at the top left of the Base Builder screen. This will show a list of buildings, along with how much they cost and their abilities.
Tap the building you wish to construct, then drag and drop it to place it within your base. You cannot undo this once the building has been placed. There will be some buildings that you cannot construct until you meet certain requirements.
If your base has run out of floorspace, you can expand Abel’s borders by tapping the green arrows along the back walls. You will need to spend some Supplies and Materials to do so.
All base building takes place within the app, but you can view your base online if you want to check your progress while you're using the website.
Please Note: If you are using Zombies, Run! with VoiceOver then the base will work differently to the description above. Please see the Base Building for Visually Impaired Users article for more information about how to use the accessible base.