There are several different complexity levels to equipping. The most basic is equipping a single item in a slot. Most things you equip are made in a Forge. To see what you have equipped, you can click on the Equipment Icon (looks like a helmet - highlighted in the image below)
Lets make a Quick Matter Knife.
To equip an item, Left Click on the item, and then select one of the equipment slots shown. Some items will have equipment slots shown that don't make a lot of sense at first. You can see that below. Choose left_arm or right_arm and the Quick Matter Knife will be equipped.
Looking back at the picture above - you'll notice that I've highlighted in green a button that looks like a helmet. You click that to open/close your
equipment display. You'll also notice that on your equipment display, it will show a number like 0/3 Cap Used. Each equippable item takes up capacity in a
slot. Some items take up all of the capacity, some only take up part of the capacity.
This is where surgery comes in. To equip multiple items per slot (up to the capacity maximum), and to equip things to odd places (like the Quick Matter Knife equipping into your head), you will need to be standing on an Auto Doc to have surgery done. This requires a skill check, similar to manufacturing. In the picture below I am standing on an Auto Doc. If your surgery skill is low, and the combination of items is complex, you may fail the surgery, which will damage you and destroy all items in the slot.