The best part about coloring digitally is there are so many ways to do it. This can seem like a daunting challenge at first, but it means that no matter what skill level you're at, with a bit of practice and experimenting, you're bound to find a method, technique, and style that works for you.
Some people paint on one layer. Some people color their lineart. Some people color over the original sketch. Some people use masks, whereas others use clipping groups and locked layers. Some people end up having 2 or 3 copies of the illustration as separate layers for things like color dashing and lighting rendering, others don't even shade and only use flat colors.
I think my best piece of advice for this would be to look up some tutorials. Even just searching specific tutorials like "painting skin", "painting hair", "painting backgrounds", etc. even if it's not the subject matter you're looking to paint will get you some awesome tutorials from Tumblr, DA, etc. that will give you some great tips and techniques for painting in general. There are also places like CTRL+Paint which are 100% devoted to providing tutorials for digital painting and rendering (there's also CG Cookie but you typically have to pay for their tutorials and lessons.... they're really good though).
Starting off simply, I'd suggest just looking around for a digital drawing program. My personal favorite is Clip Studio Paint, but if you're tight on cash, programs like FireAlpaca, GIMP, and Paint Tool SAI (I think this one requires payment too but it's much cheaper and I'm sure there are some free alternatives out there lol) will help you get the job done.
Once you get your hands on a program to use, just test out the interface. Experiment with layers, brushes, opacity, etc. Doodle lots. Once you've gotten the hang of how one drawing program works, you've got the basis to every single other drawing program out there (it all comes down to a similar design, but different programs do have different additions - ex. Photoshop CS6 has lots of photo editing tools, whereas Clip Studio Paint comes loaded with panel rulers and template guides, as it's a comic creating software).
If you're looking to work traditionally, you can always color using your preferred coloring tools and scan your work. Additionally, you could do your inking with traditional pen, and scan it into Photoshop, and do the coloring digitally (I know that's how Postcards in Braille does it last time I checked, and they do a remarkable job of it).
Honestly though, just have fun with it. Coloring is always fun when you step out of your comfort zone and with all the ways you can do it and all the possible outcomes, it's super hard to not find something that works for your personal tastes and style. Just have fun with it, don't get discouraged, and don't be afraid to take advantage of the hundreds of thousands of user-made and professional tutorials out there.