The genes for red hair are very common in the population, but they are recessive (meaning that they are dominated by any other hair colour). So if you have some genes for brown hair and some genes for red hair, you will end up with brown hair yourself. If you have children with someone else with the same gene mix, there is a one in four chance that your child together will have red hair. This often comes as quite a shock to people with no obvious history of redheads in the family.
The pigments in hair are made up of different types of melanin. The main types are eumelanin , which is brown, and phaeomelanin , which is red. Somebody with dark hair has mostly eumelanin . Somebody with very bright red hair has a little eumelanin but lots of phaeomelanin. People with auburn hair will have some of both types of melanin.
Red hair is interesting because it is particularly likely to change hue over the years. Also, it can be a bit variable over the body; notably, sometimes men with brown hairon their heads have red beards. Some blond babies turn into redheads by the age of 5, while some redhead babies fade to dull brown hair by adulthood.
Red hair is a recessive trait. This means that you will have to have inherited the allele for red hair from BOTH parents so that you are purebreeding recessive for your ginger hair.