If you're an image taker, you should care about your images from start to finish. Sometimes we hand off our images to someone else for finishing, and sometimes we handle those things ourselves. This article is for the latter.
For those who prefer the old school route of reading a book, this is a recommended text:
Correction & Grading are not the same thing
First thing to know is that Color Correction and Grading, are separate processes. Correction is just what it sounds like: correcting the image so that it is well balanced and has as few artifacts/color casts/etc... as possible so you have the cleanest starting point for Grading. Grading is where the choices are made as to how the image will be styled. Will it be bright and cheery, dark and moody?
You're right, you made a lot of those decisions when lighting & shooting those images, but if you shot a flat profile such as log (which, 9 times out of 10 is the accepted thing to do these days) Then you have room for many decisions to make as to how your final image will look.
What program to use?
There are a number of tools you can use to grade your images, some of which are built into your NLE. There are plenty of opinions about which software is best, but it boils down to the same old mac vs pc type debates. My recommendation is to use the tool that makes the most sense for you.
If you're already an Adobe CC member, try Speedgrade which i've included a tutorial to at the bottom of this article. If you're on Final Cut, there are tools built in. Davincii Resolve is a popular standalone software and is actually free for most of the functionality. As always, don't base your decision on hype or fanboys, but on reasoned points.
Starting with color correction
I recommend reading through this fantastic writeup by Vashi Nedomansky, on Shane Hurlbut's site: 7 Tips for HD Color Correction and DSLR Color Correction
It is well broken down and gives a nice overview of the order of workflow in correction and grading. I'll leave you with that one example because many of the following tutorials touch on the same concepts.
Color correction will seem fairly strait forward when compared to Grading, which is where the magic happens. Grading can happen in quite a few different programs, as such, i have several recommendations for where to get started and really dig in. Note that since a lot of the tools are identical, watching through several tutorials will result in an overlap of information. This is good though, it will help it sink in and you'll see how different colorists use the same tools but in different combinations and with different intents.
First up, this Davinci Resolve tutorial by GranolaTech actually touches upon both correction and grading. In a short span of time you'll see much of the overall toolset that gets used for both processes.
My next suggestion is to watch through Chris Hall's series "Anatomy of a Grade"
Through much of the series you won't even see a grading program, but he talks you through what he's doing to the images with his methodology which will give you a great understanding of what a colorist looks for and executes. Later on in the series he shows you the work in Davincii Resolve, and goes into more advanced topics such as masks.
Although we're talking about film/video, this tutorial in the Photoshop Training Channel goes into nice detail on Grading
Many of the tools used in Photoshop are just about the same as what you would use in other video-centric software. They aren't organized in quite the same way, but this video will give you a nice overview of their uses.
Finally, for those of you who wish to skip lunch, here is a near 2 hour introduction into Adobe Speedgrade. A lot of it is just learning the software vs actual grading methodology. This isn't to say that speedgrade is the program to choose, but knowing the ins and outs of a program is very helpful in learning the overall process.
Assuming you have quality footage to work with, you can do amazing things with color grading. My default answer to a producer who asks about color grading, is that if they want the most of their footage, hire the best colorist they can afford. A true specialist is worth their salt, but many of us shooter/editor folks can do a lot on our own with the vast amount of information available to us for learning.
Above all, care about your images. Anyone can make a video, but only those who want the best, achieve the best.