Among several options for shading and tinting:
For shades, multiply each component by 1/4, 1/2, 3/4, etc., of its previous value. The smaller the factor, the darker the shade.
For tints, calculate (255 - previous value), multiply that by 1/4, 1/2, 3/4, etc. (the greater the factor, the lighter the tint), and add that to the previous value (assuming each.component is a 8-bit integer).
Note that color manipulations (such as tints and other shading) should be done in linear RGB. However, RGB colors specified in documents or encoded in images and video are not likely to be in linear RGB, in which case a so-called inverse transfer function needs to be applied to each of the RGB color's components. This function varies with the RGB color space. For example, in the sRGB color space (which can be assumed if the RGB color space is unknown), this function is roughly equivalent to raising each sRGB color component (ranging from 0 through 1) to a power of 2.2. (Note that "linear RGB" is not an RGB color space.)
See also Violet Giraffe's comment about "gamma correction".