How do I determine darker or lighter color variant of a given color?

In XNA there is the Color.Lerp static method that does this as the difference between two colours.

Lerp is a mathematical operation between two floats that changes the value of the first by a ratio of the difference between them.

Here’s an extension method to do it to a float:

public static float Lerp( this float start, float end, float amount)
{
    float difference = end - start;
    float adjusted = difference * amount;
    return start + adjusted;
}

So then a simple lerp operation between two colours using RGB would be:

public static Color Lerp(this Color colour, Color to, float amount)
{
    // start colours as lerp-able floats
    float sr = colour.R, sg = colour.G, sb = colour.B;

    // end colours as lerp-able floats
    float er = to.R, eg = to.G, eb = to.B;

    // lerp the colours to get the difference
    byte r = (byte) sr.Lerp(er, amount),
         g = (byte) sg.Lerp(eg, amount),
         b = (byte) sb.Lerp(eb, amount);

    // return the new colour
    return Color.FromArgb(r, g, b);
}

An example of applying this would be something like:

// make red 50% lighter:
Color.Red.Lerp( Color.White, 0.5f );

// make red 75% darker:
Color.Red.Lerp( Color.Black, 0.75f );

// make white 10% bluer:
Color.White.Lerp( Color.Blue, 0.1f );