Ian Plant has a brief article on photographing rainbows. It’s mostly pretty intuitive stuff, though his advice an using just a little (not too much) polarization is helpful. But the images in the article are fantastic! Ian has been a lucky man in the realm of atmospheric phenomena.
My own two cents would be that, in this regard, you make your own luck, and for rainbows that means spending a lot of time out in crummy weather. This is good advice for photography in any case: when I see a “perfect” weather forecast, my response is to plan on catching up on chores around the house.
I’ve certainly seen some terrific rainbows over the years, including one near Salmon, Idaho that looked like a new-age poster: tawny hills bathed in honey-colored light, a huge double rainbow and (seriously) a redtail hawk soaring through it. If I’d actually captured an image of that scene, I’d be pilloried for tasteless abuse of Photoshop. But a lot has to come together to actually photograph the things, and I really haven’t got much in the way of rainbow shots. Here’s my closest one, from last summer on the Stoddard Trail in Idaho’s Frank Church Wilderness. The canyon on the right is the Middle Fork of the Salmon coming to join the Main Salmon on the left. There are a number of factors which prevent this from being a keeper, but it still has plenty of appeal: