Equipment can be bought from stores, looted from containers, or taken from defeated enemies. Equipment from enemies will be automatically added to your inventory; there is no need to stop and search corpses.
Press [ I ] to access the Equipment Screen, which consists of several "boxes" next to an image of the currently selected character.
The bottom row lists the squad's consumable Resources: current and maximum supplies of medi-gel and grenades, available omni-gel, and available credits.
Above Resources is the main inventory box. The top row of icons allows you to switch between different types of equipment: Assault Rifles, Biotic Amps, Armor, etc. Below is a scrolling text list of your equipment within the currently selected type. Items which are shaded grey cannot be used by the currently selected character.
At the top left is a box showing the stats of your currently Equipped Item of the active type. At the top right is a second box showing the stats of the currently Selected Item in the inventory box, allowing at-a-glance comparison. To equip the selected item, double click its name in the Inventory box or use the Equip button at the bottom.
Your Equipped Item in the top left will display one or more light blue squares. These are Upgrade Slots. Upgrades enhance equipment capabilities in various ways. Click on an Upgrade Slot to switch the Inventory box to display Upgrades that can be equipped in the current piece of equipment. Click the icons at the top of the Inventory box to switch between the Upgrades Slots on the item.
Unneeded equipment can be sold for credits at a vendor, or reduced to omni-gel using a button at the bottom of the inventory box.