Always purchase single pigments to save money and make your palette more versatile. If you get familiar with the coding on the paint tubes look for the color index codes. If you see more than one code, it is a mixture. The first two letters stand for the type of color (PR means Permanent Red) and the numerical code tells you the kind of pigment. Find a chart at your art supply store or online, most companies have charts for your reference. See picture below of what to look for.
To make a very good visual black, mix ultramarine blue with cadmium red dark or maroon. If you do not have the dark version of cadmium, a medium will do. The opacity of the red, along with its orange bias creates a very strong visual black with good coverage. This is my favorite, it is easy and vibrant.
The lightest colors on your palette are yellow and white. Since yellow is already so light, it is difficult to lighten it even more. The best way is to start with a clean brush and some white on your palette, slowly mix in just a tad of yellow at a time, until you get the color you want. If you mix white into yellow it takes too much paint to really lighten the yellow. If you decide to use yellow to paint florals over a background, make sure you use opaque pigments. Use cadmium or a yellow with plenty of titanium white added so you cover the background color. Transparent yellows can almost disappear over a vivid background.
For that matter, always add the darker color to the lighter color, a little at a time. It takes much more light color to change a dark one and you could end up with way more paint than you need of a mixture. Save paint and time with this tip.
Always add a bit of warm color to white for highlights such as light on glass or water. Use the warm colors that are on your palette (yellows and maybe a tiny touch of light red) to warm the white.
You can make numerous types of browns, grays, and tans using red, yellow, blue and white. Decide what bias you want your final color to be. Do you want a blue gray, a red or orange brown, and light yellow/tan color? Then start with that primary color, or mix a secondary color using two pigments. Add a little of the third primary in small increments until your color is achieved. If you want a lighter version, add a little white, just a little at a time to get the value you want.
Mix into the edge of your mixtures, not right in the middle. That way you can control the variation. A palette knife is good for mixing if you know what you are doing, and want a lot of a color. Otherwise, practice mixing with a brush, and take off excess paint before you mix, just try a little at a time. You can ALWAYS recreate a color. Trust your eyes to see the main ingredients in your desired color. This will tell you where to start. Practice is what you need to be able to really see color. If your brush contains white in the bristles, that white will get into your mixture, so be warned, you cannot get it out. Use clean brushes and plenty of them!
Look at the VALUE (how light or dark it is compared to the other colors) of the colors on your palette to help you decide which colors to choose when mixing. If you want a dark color, go for the darker pigments.
Sticking with a limited palette will produce a painting with color harmony. It is a sure thing!