Yesterday, on a forum, I saw a common lament. The member had a photo with a broad blue sky, and was complaining about the banding evident in it.
Banding is such a tricky beast, mainly because it's darn hard to tell whether it's genuinely in the image, or if it's just your screen. This makes you as nervous as hell, because you are wondering if it will occur in print.
As it happened, I couldn't see the banding on my screen in this particular photo that had been posted. This caused me to suspect that it was just the guy's screen that was showing a non-existent problem. I asked him for details of his monitor, and sure enough, it was a fairly cheap TN panel, which are prone to this kind of thing. (Ironically, it seems to occur more prominently in a calibrated screen than an uncalibrated one.)
If you are ever worried about banding in one of your images, here's a simple test for you - apply a generous dose of gaussian blur to your image. If the banding disappears, then it was in your image. If the banding remains, or gets worse, it's your screen.
Another helpful option is just what the photographer in my tale did - post your photo somewhere and ask other people to look at it. If everyone says they see banding, then maybe you've got a problem. But if some people say it looks fine, then it's probably just your screen.
If the problem is just your screen, don't sweat it too much. Well, keep putting away your pennies for a better screen, but for now, you should be able to get a test print done with reasonable confidence.
If the banding is in your image, you have two approaches. First, you could start again with your Raw file (assuming you have one) and work in 16-bit instead of 8-bit. The whole purpose of high-bit is to prevent banding. Plus, make sure you do as much of your editing in Raw as possible, and limit the amount of tweaking needed in Photoshop. Raw data doesn't get visible banding - it only occurs once the raw data has been converted to an image file, and adjustments are made thereto.
If you don't have a raw file to work from, or if you simply can't face re-processing, then the answer is noise. Some people try to blur to get rid of banding, but that doesn't work. The trick is actually to apply a small amount of noise (1-2% is enough) to the sky.
Of course, there's a caveat to all of this. Even if your file is beautiful and clean and banding-free, there's still a chance that there will be banding in the print, due to limitations of the printing process. If that happens, speak to your lab about how best to handle the situation. If you're intending a big expensive print, and you have suspicions about banding, it might be a good idea to get a smaller test print done first, as I described here.