Using the board is simple - simply click on the square for what you want and a new page opens. Choices that are light are currently unavailable, choices that are dark are currently available. A dark colored odds box means odds for that particular track are currently available. So, in the Belmont Park bar above, the odds are currently available. But Quinella and Results are unavailable at the current time.
Daily information is found on the toteboards.
If you want past days' results, you'll need to check the Results Archive, where you can find results as far back as August of 1998. Entries for the current day are usually posted around 9 AM EST daily. To the surprise of many, wagering on pari-mutuel events, such as thoroughbred, harness, quarter horse, and greyhound racing, is not like wagering at a Casino. Pari-mutuel wagering means that you and other bettors wager amongst each other into common pools, not against the track. In fact, the track has no interests in the results of the race, and deducts a statutory commission from each dollar wagered.