Well, there are numerous programs or plugins you can use (sometimes it depends on the platform you work on and sometimes on the NLE you use).
For starters (about contrast): make sure you understand how levels work and what a histogram tells you. I know this is more like a photoshop tool, but it will help you understand your image. (Eventhough for example the histogram in Premiere Pro is a bit useless: little amplitude is shown. But in After Effects you can see a lot more info. Btw, a histogram tells you how much dark, light and mid tones are present in the image.)
This is the simple way.
Experiment with curves:
it's effect is (a bit) similair to levels, but the graphs look different.
A more technical approach involves waveforms on the scopes and setting black, white and mid levels. This may sound difficult, but when you understand the histogram and levels, it all makes sense within a few minutes.
I have Color Correction for Video (S. Hullfish & J. Fowler) on my bookshelf and it's a great resource on the subject. It won't tell you what to do, but it tells you how things work.
Videotutorials are a great resource, but I find 260 pages on the subject (really the subject, not tutorials on how software works) really usefull.
For quick simple things I often use levels or curves.
It also depends on where I'm working: on my own computer I like to use Colorista (also for quick gradients) and Magic Bullets Looks (for certain looks). On location at a client these tools are not always available.
About color:
There are a lot of tools to change the color/feel of an image.
Sometimes you just want to make it warmer or cooler.
Try using color balance (RGB) and see what is does.
Try using HLS (hue, lightness, saturation) and see what it does.
Watch the recommended tutorials, but I advice you to experiment a little bit before watching them. This way you will also understand what you may have done 'wrong' and what you can do next time. Otherwise there is a chance you watch a lot of stuff and you get puzzled by all the functions they show. If you have seen them before, it will make it easier to understand.
Good luck!