Accurate as of version 0.35.02 2/3/2023

Select someone with a high skill in Computer Science (the higher the skill the faster they will upgrade/build) and right click the "block terminal" (it is the panel on the floor with the swirly design) in the center of a room.
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After which a menu should pop up with all your installed objects (you must first build and install an object before you can upgrade it.)
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Left click the object you wish to upgrade and here you will now see the selectable upgrades under a picture of the selected object. For example, I will be selecting the Kitchen in this Crew Quarters block module.
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Note that objects with no upgrades will show nothing below the picture. This is normal!