The best place to start is to find a color wheel. Let's say you want to use red but you're looking to brighten up the color. Beginners will want to add white. This is fine if you are looking for a pink tint. The best way to do it is to add a little bit of the color next to red on the color wheel. In this case it would be orange.
Now let's say you want to darken that red, do you add black? No. Why? Well, if you add black the color will lose it's vibrancy and become dull. So what should you do? In this case if you want to darken that red find a darker color that is next to red. We can see in the picture above that it's magenta/purple! (Analogous Color)
What if you want to tone down the vibrancy? This is where it becomes tricky. You could add grey but where's the fun in that?! What I do is I use the color on the opposite end of the color wheel, so if we want to tone down that red we would add a green. (Complimentary color)
If you are looking for a pastel by all means add white! If you are looking for neutral colors, just add grey! Oh and btw if you want to mix the best vibrant black, my hack is to mix a cad red with a Phthalo Blue! Don't take my word for it, go learn about color theory! It takes some time but once you catch on, it's like magic!!