Climate control is important when storing furniture. Without climate control, stored furniture is subject to not merely fluctuating temperatures, but humidity as well. Humidity can cause moisture buildup that can lead to mold and/or finish damage.
Furniture that is stored should be covered. Covering furniture with cloth tarps will help protect it from dust, dirt and debris. This is of particular importance with upholstered furniture because dust and dirt can lead to discoloration and staining.
It is important to store your belongings so they are raised off the floor. If there is a flood, this measure will protect your belongings from getting wet. Even when you store your furniture on higher levels of a storage building, flooding is still a possibility---a pipe could burst, or a fire sprinkler could go off. Furniture that is covered and raised has less chance of suffering water damage.
To make unpacking your storage unit easier, try to keep together furniture pieces that go in the same room. That way, if you need to get one room out and leave one room stored, you can do so with less hassle. Make sure to leave room for airflow between furniture pieces.
Take apart any furniture that can be disassembled. Store the parts together and label everything well. Furniture that is disassembled not only takes up less space, but it is less likely to become broken when it is being moved or stored.
Regardless of the reputation of the storage facility you use, accidents can happen. For this reason, it is important to insure the furniture you are storing. If the insurance is offered individually, make sure to check your contract and/or ask about the insurance before moving your belongings in. Also, depending on the value of your items, you may want additional coverage above the automatic coverage.