To access the warehouse, just go there and use the storage container. This works the same as a bank in other MMORPGs. You can move items in and out of the warehouse by accessing the storage container. You cannot access your memory anywhere else in the world. To use it, you need to stand by the storage container.
Storage capacity is based on weight, not number of items (similar to your character's inventory), so you're limited on what you can store in your storage.
Remember that your storage is localized (unless you have connected territories - see below). This means that each settlement has a different warehouse. For example, you run to the settlement of First Light and place 200 ore in this warehouse. Then you go to Everfall. While in Everfall, you use a storage container in this settlement. The 200 ore you store in First Light won't be there as it is in the First Light warehouse and not the Everfall warehouse. So the only way to get these 200 ore would be to go back to the First Light and retrieve it from the First Light warehouse.
Connected warehouses via connected territories
Any two settlements controlled by the same faction will have the settlement stores connected. Players can transfer items from the storage associated with their current location for a fee in the form of coins. If the territories are not connected, your storage is located as described above.
You can increase the storage capacity of each settlement by increasing your position in a given territory and selecting a storage capacity bonus. When you expand your capacity in one territory, it only applies to that territory. This is not a global increase for every warehouse location.