If you're going to climb a rainbow, you need feather shoes. I prefer goose down shoes -- but any small feathers made into shoes will do.
Ideally look for the cool kind of rainbow that happens as early in the morning. Without any residual heat or glare from a whole day interfering with your climb, it should be simple to go up the side.
Handle the rainbow carefully, don't crimp or put dents in it as you go, or you could get lightening or scattering that makes the rainbow go away.
You can stop at the top, enjoy the view, then slide down either side.
I heard that some folks ride the top of the rainbow as it moves through the sky. I have not tried that yet, because I need to get more confident in my climbing technique and having that feeling on how long the rainbow will be around.