Color has value and it is useful to be very conscious of this.
Each color has a native value at its full intensity. You can lighten and darken the value by adding white and black. However, you run into a problem with this. White and black dull a color. There are two ways to lighten a color: using white or using an analogous color. Yellow, which is lighter than orange or red, will lighten them. Yellow will also lighten green. If you can’t use yellow (a high-key color), you can use a procedure called glazing to correct a color that has been lightened (and dulled) by the addition of white.
Glazing will be discussed later. It fell out of use in the impressionist era but I believe it is very useful. There are “off-the-shelf” glazing mediums that you can buy, such as Liquin (from Winsor Newton), a fast-drying medium, for oils or matte medium for acrylics. Generally, with oils, your only restriction is that you must allow enough drying time before glazing.
You can use some darker colors that are analogous to darken the native hue of a color. For instance, Alizarin Crimson will darken Cadmium Red without losing the redness of it.
To familiarize yourself with the basic value of the colors on your palette and improve your understanding of how to lighten and darken them, I recommend the following exercise.
Do a value scale (from white to black) across the top of your page or canvas. Take each of the colors on your palette and, on separate rows under the black and white value scale, place the fully saturated color (generally the color as it comes out of the tube) at the correct point on the value scale. (For instance, even a full hue of yellow would fall towards the white end of the scale, while blue will fit towards the black end of the scale.) Then, for each color, work back and forth on the value scale, towards white by adding white or an analogous color, and towards black by adding the complement of the color you are exploring. As a final check, take a black and white photo or take the completed exercise to a copying machine and make a copy in black and white.