If you don't know much start by reading 'Horse Heaven' by Jane Smiley. It gives a nice overview of the whole industry. The book is fiction but it's well researched.
The main online sites are....
(good articles for newbies)
(very technical though)
The websites are really industry specific. They are difficult to read if you don't know the language and history of racing. You could always go to the races but make sure you go with someone who knows what is going on. If you live in N.America I would be happy to take you to the track.
This Saturday is a big day in racing, Smarty Jones is trying to win the Belmont Stakes meaning he will win the Triple Crown. The Triple Crown (TC) is a series of races that starts with the Kentucky Derby then the Preakness (I watched this as I nursed my daughter in the hospital hours after giving birth) and finally the Belmont. Only about 10-15 horses in the history of racing have won the Triple Crown. There is NOTHING more prestigious on this planet in horseracing. Most people think the TC has more to do with God, fate and destiny than actual horses, jockeys and trainers.
Also in England (I don't know what your focus is) this weekend is the Epsom Derby. It is a VERY prestigious race. Following the Epsom Derby is Royal Ascot and then something else after that-I forget.
But at the end of the season in October is the Prix de Longchamp in Paris and the Breeders Cup in the US. These two end of season races are essentially where the best horses of the season go at it for the last time before being given a winter holiday. It is my opinion these are two of the best races being run on the planet.
Okay, this is probably way too much information....I don't mean to flood you with information but I love racing. I'm more than happy to help you out-just let me know.