If you've recently moved from a dry climate to one that is humid, you'll need to take some measures to prevent rust, musty odors, and dust mites from affecting the items in your garage. Here are a few things you can do. 

Use Desiccant Packets

Desiccant packets contain moisture-absorbing silica gel, which can reduce the amount of moisture in your garage. Here are 3 ways to use desiccant packets. 

1. Prevent Rusty Metal—The humidity in the garage can cause your tools and other metal items to become rusty. The moisture in the air causes the metal to oxidize, which leads to the formation of rust. Place packets of desiccant in your tool drawers to control moisture. Store metal items in plastic storage containers and place a desiccant packet or two in them. 
2. Prevent Musty Odors—Excessive moisture in a humid garage can cause musty odors in fabrics and other porous material, such as the concrete floor. The interior of a vehicle stored in your garage can also cause an overwhelming musty odor. Desiccant packets can remove the moisture that causes musty odors to form. Place several packets inside your stored vehicle, such as in the cup holders and in the trunk. Hang large desiccant packets in the garage. Any cardboard boxes that are used for storage should have at least one packet thrown into each box. 
3. Prevent Dust Mites—Dust mites thrive in humidity and feed off of flakes of skin, which makes your garage an ideal breeding ground if you store items such as comforters and clothing in your garage. Place all items that have come in contact with a member of your family, humans and pets, in plastic storage bins or vacuumed bags along with packets of desiccant. 

A company like Interteck Packaging can be a great resource for getting plenty of desiccant packets for your storage needs.

Control ground water 

It's important to understand that the concrete flooring of your garage is porous, which means moisture from the ground water under the garage can seep through the concrete and add to the humidity problem in your garage. One way to prevent ground water from affecting the humidity level in your garage is to install a French drain around the perimeter of your garage. A French drain consists of perforated pipes and gravel placed in a trench to direct ground water away from the garage and to a storm drain or to an area away and down a slope from the garage. Alternatively, the French drain can be connected to an existing garage floor drain, if available.