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

HSV ( Hue / Saturation / Value ) also called HSL ( Hue / Saturation / Lightness ) is just a different color representation.

Using this representation is it easier to adjust the brightness. So convert from RGB to HSV, brighten the 'V', then convert back to RGB.

Below is some C code to convert

void RGBToHSV(unsigned char cr, unsigned char cg, unsigned char cb,double *ph,double *ps,double *pv)
{
double r,g,b;
double max, min, delta;

/* convert RGB to [0,1] */

r = (double)cr/255.0f;
g = (double)cg/255.0f;
b = (double)cb/255.0f;

max = MAXx(r,(MAXx(g,b)));
min = MINx(r,(MINx(g,b)));

pv[0] = max;

/* Calculate saturation */

if (max != 0.0)
    ps[0] = (max-min)/max;
else
    ps[0] = 0.0; 

if (ps[0] == 0.0)
{
    ph[0] = 0.0f;   //UNDEFINED;
    return;
}
/* chromatic case: Saturation is not 0, so determine hue */
delta = max-min;

if (r==max)
{
    ph[0] = (g-b)/delta;
}
else if (g==max)
{
    ph[0] = 2.0 + (b-r)/delta;
}
else if (b==max)
{
    ph[0] = 4.0 + (r-g)/delta;
}
ph[0] = ph[0] * 60.0;
if (ph[0] < 0.0)
    ph[0] += 360.0;
}

void HSVToRGB(double h,double s,double v,unsigned char *pr,unsigned char *pg,unsigned char *pb)
{
int i;
double f, p, q, t;
double r,g,b;

if( s == 0 )
{
    // achromatic (grey)
    r = g = b = v;
}
else
{
    h /= 60;            // sector 0 to 5
    i = (int)floor( h );
    f = h - i;          // factorial part of h
    p = v * ( 1 - s );
    q = v * ( 1 - s * f );
    t = v * ( 1 - s * ( 1 - f ) );
    switch( i )
    {
    case 0:
        r = v;
        g = t;
        b = p;
    break;
    case 1:
        r = q;
        g = v;
        b = p;
    break;
    case 2:
        r = p;
        g = v;
        b = t;
    break;
    case 3:
        r = p;
        g = q;
        b = v;
    break;
    case 4:
        r = t;
        g = p;
        b = v;
    break;
    default:        // case 5:
        r = v;
        g = p;
        b = q;
    break;
    }
}
r*=255;
g*=255;
b*=255;

pr[0]=(unsigned char)r;
pg[0]=(unsigned char)g;
pb[0]=(unsigned char)b;
}

Simply multiply the RGB values by the amount you want to modify the level by. If one of the colors is already at the max value, then you can't make it any brighter (using HSV math anyway.)

This gives the exact same result with a lot less math as switching to HSV and then modifying V. This gives the same result as switching to HSL and then modifying L, as long as you don't want to start losing saturation.

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 );

Rich Newman discusses HSL color with respect to .NET System.Drawing.Color on his blog and even provides an HSLColor class that does all the work for you. Convert your System.Drawing.Color to an HSLColor, add/subtract values against the Luminosity, and convert back to System.Drawing.Color for use in your app.