Skinheads were originaly working class kids, growing up in the early Ska era. They started cutting their hair and shaving their heads because they got into alot of fights at local soccer games and long hair was getting in their way. The fights got bad enough that anyone wearing steel-toed work boots was not alowed to watch the games. The boots were a large part of Skinhead fashion, which also included tight work jeans and braces (suspenders).
Skinheads picked up a reputation for racism long before nazi's and neo-nazis were around, starting with National Front Skinheads, who got upset about immigrant workers taking factory jobs. Neo-Nazis picked up on skinhead fashion because of the skinheads being well known for their ability to fight, and to target working class kids for recruitment. There are still groups of skinheads that call themselves "hammerskins" today that are racist and very elitist, and continue to give skins a bad reputation. I believe racism and skinhead values to be contradictary because of the background in working class and unity, and the fact that all cultures or races have some sort of lower or working class.
Oi music is another strong part of skinhead culture, and is the skin version of punk rock. The music is often slower and more melodious. The term Oi comes from a traditional Greek greeting "oi polloi" and from the cockney adaptation to mean simply "hey". Skinheads are another big part of English and Jamaican ska history, as seen in songs like "Skinhead Moonstomp".
Skinheads are also rather well known for their love of drinking, as "Work is the Curse of the Drinking Class" - Oscar Wilde.