When you're talking about "flat color", are you referring to a lack of contrast? Desaturation?
Really in either case, unless you've planned for a lot of work to be done in Post, it's best to get things as close as you can in camera, while still maximizing color data.
Since it sounds like the footage is already shot, though, I'll run you through a basic color-correction workflow, but keep it as vague as I can because I'm not sure what software you'll be using.
1) I like to pull in a levels adjustment so that I can set my black and white points, you can either do this by looking at the histogram and scrolling through the timeline or by looking at a section of the image that you want to set as your extremities and picking it with an eyedrop color selection tool. I prefer to use the histogram so that I can leave myself a little extra space to play with in step 2.
Some people instead like to use a shadow/highlights adjustment instead depending on where you're correcting, but I find the levels to be more universally available, so it's what I'm used to.
2) Secondly, to set the contrast I want and take basic corrective measures, I slap on some RGB Curves. These are incredibly powerful, and some people can use these to accomplish far more than I, but I just use it for contrast and cast correction. First use the RGB Curve and apply a gentle "S" to it, dipping the low tones (usually the lower left corner of the graph)a little lower and raising the highlights to whatever your style requires.
Around this point you'll be able to see if you have a color cast on your image (usually blue, orange, or green). Blue indicates that a cool light source (daylight, certain headlights) influenced your image, orange that a warm light source (incandescent bulbs, usually) influenced your shot, green usually indicating either that a fluorescent influenced the shot, or that you're in the Matrix. Adjust the color curves as necessary to balance the image to a nice, neutral state.
3) Now that your image looks balanced, feel free to leave it like that if you want, you should have a nice, natural-looking, balanced image. If you want to take it a bit further, however, you can toss on some variety of Three-Channel Color Corrector. At this point, feel free to use the Lift, Gamma, and Gain controls to add a hint of a color scheme to your shadows, midtones, and highlights. Just remember to leave your skintones in the orange/pink range. To finish it off, feel free to use a saturation control to either bump up or down the saturation a bit, but avoid going too far in either direction as it tends to be the hallmark of an amateur.
That's a really easy post color workflow to start with, and it should be able to take you pretty far. Once again, however, to avoid having to spend too much time working on every shot to get what you're looking for, I highly recommend getting what you need in camera.
If that doesn't take it as far as you need to go, then you might want to consider a re-shoot. It's definitely possible to take color much further than this in post, sure, but if you have to save every shot via post, then not enough work was done during the shoot to get what you need.
