The ME Chest acts as a basic storage system for an ME network. It allows you to place an ME storage item in it to access whatever's in that item quickly. You may connect it to your network via ME cable, though it only needs a small amount of power to run (which is obtained from the ME controller)
The chest may also be accessed via an ME access terminal or an ME wireless access terminal if an ME wireless access point is within range. You will not be able to access other networked chests without using an access terminal connected to the same network. This makes the ME drive a much better - but more costly - storage system for the network. The chest acts somewhat as a normal chest, allowing you to open it and access the items inside it. It requires an ME storage item in it, however, and will not work without one. The storage item goes in the top right slot, shown in the images below. The storage area will be greyed out and inaccessible until a storage item has been placed inside it (also shown below)
After a storage item has been placed inside the chest, you may freely add and remove things to and from the chest, up to whatever limit the storage item has placed upon the chest.