How to use curves to colour grade video
Inspector > Colour in Video by Zaweba has master and RGB curves, hue curves and a secondary key. Here is how to use them to grade footage.

Curves live in Inspector > Colour in Video by Zaweba. There is a master curve for overall brightness and contrast, separate red, green and blue curves for colour, a set of hue curves for targeting single colours, and a secondary key for changing one range of hue, saturation and brightness on its own. Together with the shadow, midtone and highlight colour wheels, they cover most grading jobs.
Curves look technical but the idea is simple. The bottom left of a curve is the darkest part of the picture and the top right the brightest. Push a point up and that part of the picture gets brighter; pull it down and it gets darker. Everything between bends smoothly.
The master curve
Start here. A gentle S shape, pulling the shadows down a little and lifting the highlights a little, adds contrast and makes flat footage look richer. Pulling the bottom left point upwards lifts the blacks to a faded, matte look. Lowering the top right point softens harsh highlights.
Small moves go a long way. If the picture looks crunchy or strange, the curve is probably too steep.
Red, green and blue curves
These change colour by brightness. Lifting the blue curve in the shadows and lowering it in the highlights gives the familiar cool shadow, warm highlight look. Pulling green down slightly across the middle removes a greenish cast from indoor lighting. Because each curve affects only one channel, you can correct a colour cast in the shadows without touching the highlights.
For broader moves, the colour wheels are quicker: push the shadow wheel towards blue and the highlight wheel towards orange for the same look with less fiddling.
Hue curves
Hue curves pick a colour and change it. Hue vs saturation turns one colour up or down, so you can make the sky bluer without making skin redder. Hue vs hue shifts one colour into another, nudging a yellow-green lawn towards a fresher green. Hue vs brightness makes one colour lighter or darker. Brightness vs saturation and saturation vs saturation control how colourful the shadows, highlights or already vivid areas are.
Secondary correction
When a curve is too broad, use the secondary key. It selects pixels by a range of hue, saturation and brightness, and applies its own hue, saturation and brightness change only to them. Switch on the key view to see what is selected, refine the range until only the right area shows, then make the change.
A sensible order
Correct before you style. First get exposure and white balance right with the basic controls or Auto colour, which sets white balance and levels from the frame. Then use the master curve for contrast. Then RGB curves or wheels for colour balance. Hue curves and the secondary key come last, for specific fixes.
Use the scopes. View > Scopes shows a waveform, RGB parade, vectorscope with a skin line and a histogram. They show what your eye might miss, such as clipped highlights or a skin tone drifting off the skin line.
Grade a section at once. An adjustment layer from the Graphics menu carries a grade over every track below it. Correct each clip individually, then put a shared look on the adjustment layer.
Save the look. A grade can be exported as a 33-point .cube LUT to use on other projects or in other software.
Video by Zaweba is free software that works offline on Windows, with no account and no paid colour upgrade.