Squeaky garage doors require basic maintenance, but if your doors only squeak after it rains, you have a more specific issue on your hands. One of the biggest reason for this squeaking is that tracks attached to wood will move slightly as the wood expands due to the moisture, which is why the squeaking will start to fade over the next few days as the moisture fades. You can't stop the rain, but you can take a few steps to try to prevent as much squeaking due to moisture.
Properly Align Your Tracks
Your tracks don't need to be perfect; a minor margin of error is permissible, and your doors will still be able to open and close. But if they're out of alignment, then further movement will make the problem worse. Squeaking can come when pressure is being put on the door or tracks because the door can't glide smoothly. If you have some experience, you can try to align the tracks yourself, but if not, calling a repairman is a safe bet.
Weather Seal Your Wood and Doors
Expanding wood can cause problems for the moving parts of your garage doors, but the wood of your house isn't the only problem -- the doors themselves can also swell after a rain if they haven't been properly sealed. Many doors come with some type of weatherproofing, but if the doors are cut, chipped or modified in any way, this protection can be compromised.
To help alleviate this, you can refinish your doors and the area around the doors (such as the areas your tracks are attached to) and use a waterproof paint and seal. This will have a greater effect if your garage and garage doors are insulated, but they don't have to be. Just preventing the doors themselves from swelling during rain is a big step in the right direction.
If you opt to take on this do-it-yourself project, wait until humidity levels have been low for about a week. This will ensure that most of the moisture is out of the wood, and so swelling will be at a minimum.
Use The Right Lubricant
With an increase in moisture comes a higher risk of rust on your springs, tracks and hinges. Lubricant can help prevent this from becoming a problem, but if you use the wrong lubricant, you can cause other problems to pop up. For example, oils and greases can leave a sticky film and cause dust and dirt to build up, which hinders movement and can damage the metal.
For best results, use a silicone-based spray on all your moving parts. It lubricates without the buildup of grime, so there's no risk of buildup further hindering movement and causing damage over time. Do this in conjunction with making sure your tracks are aligned to make sure your doors are moving smoothly. Even if the rain causes some swelling, if your doors can move easily, they won't make too much noise.