Black, chocolate, and cinnamon are the most basic cat pelt colors there are. All three colors are alleles of the black fur gene. This trait is sex-linked, meaning that only a female will receive two alleles from each of their parents due to having two sex chromosomes, while a male will only receive one allele from their mother due to only having one X chromosome.

The black coloration is a bit interesting. If a cat has a solid black pelt, then their pelt will appear as black (obviously). However, if the cat is a tabby, then they will be a dark brown cat with black tabby markings (think Tigerstar). We normally just call them dark brown tabbies, but the technical term for one is a black tabby. The genetics behind tabbies will be explained in another chapter.
Black is dominant to both chocolate and cinnamon, and is represented by a capital B.

Chocolate cats are brown... obviously. The tabby version of a chocolate cat would be a lighter brown cat with dark brown stripes (think Leafpool).
Chocolate is recessive to black, but dominant to cinnamon, and is represented by a b1.

Cinnamon is also a rather interesting color, it looks a bit like ginger, except darker and has a brownish tint to it. However, they're both completely different colors, and should not be confused with one another.
Cinnamon is recessive to both black and chocolate, and is represented by a b2.

While black is an EXTREMELY common color in cats, chocolate and cinnamon are usually only found in purebreds. If you are writing a Warriors fanfiction with genetics in mind, be sure to make sure some of your cats have kittypet ancestry!

For reference, here is an image of what all three colors look like! This one is from messybeast.com

And I don't feel the need to include the images for solid colored cats since I think it's pretty self explanatory-

Fur color is a sex-linked trait, meaning that a cat's fur color is determined by the genes found in their X chromosomes. A tom normally has one X and one Y chromosome, while a she-cat normally has two X chromosomes (and I say NORMALLY because there are exceptions). This means a female cat has two alleles that decide the cat's fur color, while a male only inherits one allele that decides its fur color, since a male only has one X chromosome. The Y chromosome is ONLY there to signify that he is a tom.

With female fur color, dominance comes into play when a female inherits two different alleles. For example, if a female inherits one black allele and one chocolate allele, she would be a black cat, since black is dominant over chocolate. With males, since they usually only have one X chromsome, there is no dominance, since they can only inherit one fur color allele. 

When trying to figure out the genetics of possible kits, making a punnett square sometimes helps! This is the punnett square of a female with the alleles for chocolate and cinnamon, and a male with the allele for black fur. Here is an example of one:

So as you can see here, the she-cat's chromosomes are at the top, and the tom's chromosomes are to the left. The she-cat has the alleles for both chocolate (b1) and cinnamon (b2). Since chocolate is dominant to cinnamon, she appears as a chocolate cat. The tom is a black cat, so he has the allele for black fur, and a Y chromosome to signify that he's a tom.

Each square contains one gene from its corresponding row, and one gene from its corresponding column! Any cat with XX would be a she-cat, and any cat with XY would be a tom.

A she-cat born to these two cats would have to be a black cat. She-cats inherit sex-linked traits from both parents, and since the father has the black allele (a dominant trait), any she-cat born to him would be black. The allele for black fur masks any effects of the allele for chocolate or cinnamon fur, making the she-cat a black cat.

A tom on the other hand could either end up being cinnamon or chocolate, since toms only inherit sex-linked traits from their mothers. Their other chromosome is a Y chromosome inherited from their father, which can't contain a gene.

Hope this makes sense!