When the day to move into your self-storage unit comes, you may initially feel a bit overwhelmed. Packing up a bunch of items and moving them into a storage unit is a big task, and of course you want it to go smoothly. It certainly can — if you follow these tips on move-in day. Rent a moving truck. Unless you own a large truck yourself, it is a good idea to rent a moving truck on the day you plan to fill your storage unit.