Your possessions can have an enemy when they go into a self storage unit, and that enemy is moisture. The items should be entirely dry before they're placed inside the unit, and if storage is going to be a long-term proposition for you, or if the items happen to be delicate, you're better off springing for a climate-controlled unit where the humidity inside the space is regulated. But what about when you only need to store something for a few weeks or so?
Moisture Control Products
Take a trip to your local hardware shop and look at the various moisture control products on offer. These look like little more than open plastic tubs that are filled with chemical granules. The granules literally soak any moisture out of the air and retain it. Although they're generally intended for home use, in a section of your home that might have a temporary moisture problem, they're going to be effective inside a storage unit too. You will probably need more than one, and multiple tubs would be a good idea for a larger storage unit. Just unseal the product, place the tubs strategically throughout the unit, and that's about all you need to do. Take note of the life of the granules (which should be indicated on the packaging), since they will need to be periodically changed, depending on how long you'll be using the storage unit.
There are a couple of household products that serve the same purpose. BBQ charcoal will draw moisture from the air, and cat litter will do the same thing. These products will need to be placed in a shallow tray (or trays), so as much of the product as possible is exposed to the air. Like a specific moisture control product, charcoal and cat litter will not be able to indefinitely draw in and retain airborne moisture, so it will also need to be periodically replaced.
If the unit is a garage-style one, with a roller door that opens directly to the outside world, you need to consider moisture entering the unit after heavy rainfall. Place a number of newspapers on the ground, close to the entrance to the unit. These will soak up any rain that happens to seep inside. Be sure to inspect your unit after heavy rain, and you'll probably need to change the newspapers. Once wet, they cannot be recycled, but can usually be composted.
Since your storage needs are only short term, you don't really need to do much to prevent moisture damaging your possessions, but you will need to take these basic precautions. For more information, contact local professionals like those found at Storage Choice.