Find a place to keep your change of clothing. Do this well in advance of the start of the performance. If you're lucky enough to have a dressing room, this is an ideal spot to keep the clothing. Perhaps the theater is too small to have dressing rooms for everyone, or maybe they are too far away to get to and from in the limited time you may have. In this case, finding a set spot backstage to keep your clothing may be the best option. Make sure it's in the right area for you to easily access when you run off stage.
Lay out your clothing in a designated space. Make sure the clothing is in an easily accessible state. This means removing it from any bags, suit cases or other storage devices. You don't want to be fumbling around to open your bag when your time is very limited. Proper planning beforehand ensures this will not happen.
Move quickly and deliberately. So the performance has progressed and the time to change your clothes has come; don't get distracted by all that is likely to be going on backstage. Go immediately to your clothing. Get out of your old outfit and into your new one as fast as possible.
Find someone to check out your outfit to make sure all buttons are buttoned, zippers zipped and everything looks in place. This may be another performer or a stage hand. Pick someone who looks like he could spare a few seconds, not someone in the middle of an important task. Once you get the okay, head back on stage in your new set of clothing for a successful performance.