Key tips for making the switch:
1. Fold, don't hang, your clothes. If you do hang them, don't use wire hangers, because they will stretch out or warp your clothes.
2. Store in a cool, dry place. Not the attic or basement. The guest room closet or under the bed are good places.
3. Empty pockets and clean the clothes. I've lost sunglasses and quite a bit of money by neglecting to do this. (Of course, it can be fun to find them again the following summer, but not if you find them after you've already bought another pair of sunglasses!)
4. Remove dry-cleaning bags. You may think that storing the clothes in the bags somehow protects your clothes, but it's actually bad for them. The fabric can't breathe, and you could end up with moldy clothes. I've gotten into the habit of taking clothes out of the bags as soon as we bring them home.
There are some other good tips for performing the seasonal clothes rotation at Real Simple.
*If you have a closet like this, then....well first of all, lucky you, and second of all, you may not need to do the seasonal switch. Image from Closet Tailors.