Hand-held ammunition is stored in your character's inventory and supplied to the appropriate weapon automatically. Some weapons can use multiple types of ammunition (like Armor Piercing and standard rounds).
Vehicle ammunition is normally stored in the trunk of the vehicle and supplied to the appropriate weapon automatically. The Flail and Switchblade are the exceptions, using on-board capacitors for ammunition that can only be refiled by an Vehicle Energy Crystal or Vehicle Module benefit.
All ammunition native to your empire can be obtained from any Equipment Terminal. Vehicle ammunition is availible from the vehicle tab and can be manually loaded into a vehicle's trunk. Repair/Rearm Silos and Landing Pads distribute vehicle ammunition while you are inside a vehicle.
Ammunition boxes come in sizes of 3x3, 4x4, and 5x5 depending on the weapon. When obtaining hand-held ammunition, you can find the appropriate ammo box next to the icon of the weapon you wish to use under the "Weapons" tab. For vehicle ammunition, the lower pane of the window lists what vehicle(s) the ammunition can be used in.