Here are a few tips on how to make quick changes as easy and painless as possible:
Wear undergarments that are slick so clothes slide off easily. Running shorts work well because they grip your legs well and won't move around or bunch up, they wick sweat extremely well keeping you dry and comfortable, they stretch with your body, etc.
Don't button/fasten things any more than you have to. For example, if you're wearing a button down shirt with something on top like a vest or bodice, you only have to button the shirt down to the top of that vest or bodice, or maybe one past that. You don't need to button it all the way because the audience will never see it.
If you have any say in your costume, skirts/pants with elastic waistbands are GREAT for quick changes.
Don't wait to start taking your costume off. Once the lights go down or you get safely out of sight in the wings, start unbuttoning, unzipping, removing outer garments, etc.
Pre-set your new clothes in a manner that will make your change go quickly. You want to just grab and go. Any time you have to spend fiddling with hangers or wrestling with a costume piece is wasted time that will doom your quick change.
If possible, wear your new costume under your current costume. This is called "overdressing". If you know you have a quick change in the show, be sure to mention this to your costume designer early on and ask if she can size your previous costume a bit bigger than usual so it can accommodate the added bulk of your next costume underneath. If you have several quick changes in a row, it may be possible for you to wear two or three costumes at the same time! Another possibility would be to ask if you can wear the same shirt/pants/skirt and just change your vest/jacket/bodice. If you're an ensemble character wearing a neutral colored item, the audience likely won't even notice that it's the same one you wore in the last scene.