There are base slots for Head, Torso, Left Arm, Right Arm and Legs. These parts come from the various models of robots found in the Commonwealth. All of them can have extras added on, but some more than others. The slots are as follows:

Head

Base Head

Head Armour

Torso

Base Torso

Front Armour

Rear Armour

Misc. Upgrade

Arms (Left & Right)

Base Arm

Arm Armour

Hand (weapon)

Hand Armour

Legs

Base Legs

Leg Armour


Note that all of these slots may not be available depending on your robot's base parts. There's also a Special Mods slot, but the only mods I've encountered that fit into it are story-based and not really useful for anything else.


Depending on which mods you want to add, you may require Armorer, Blacksmith, Gun Nut, Robotics Expert or Science! perks. There's no 'upgrading' mods to speak of, just replacing them with others.There are a total of sixteen slots to work with, and customisation options within these categories are extensive. Again, depending on the base parts you choose, some slots may not be available. I'm not sure what you mean by 'how equipping [sic] works'. You can't really equip your bots with anything other than the mods I've mentioned.