One relatively painless way to start maximizing your closet and avoiding mix and matching headaches is to streamline the number of colors. This doesn't mean you need to choose only three colors to wear for the rest of your life, nor does it mean that you can't enjoy colors if they make you happy. It just means pairing down to the color families and tones within those families that you like and that, ideally, suit you.
The concept of "color seasons" that one would fit into based on skin tone, hair color and eye color is a great starting point to tackle the vast array of colors out there. Again, these are guidelines. If there is a color you love that is not on your color profile, but you feel comfortable in it and think it suits you, by all means, keep wearing it. Likewise, if your color profile contains colors you despise, don't force yourself! If you get clothes in a color you don't like, no matter how much it suits you, there are high chances you'll never wear it anyway. Do take the chance to explore and dabble with colors you had never thought of though, you could discover your new favorite color!
Once you have determined your color profile, split them into color families, and determine which of these are your neutrals and which are your accent colors. The neutrals will form the basis of your closet.
Finally, I find it helps to separate the final selection of colors (adding those you love, removing those you don't) into another two groups: your spring/summer colors, and your autumn/winter ones. Obviously some colors will fit into both categories (especially your neutrals), but this will really help you when you shop for clothes.
And there you have it! Now you should be able to create a multitude of outfits mixing and matching colors (usually the key number is three main colors per outfit), or creating tonal monochromatic looks in various hues.