Here's a few starters. Go to
www.drf.com and you can learn there.
WIN bet - you collect only if your horse comes in first
PLACE bet - you collect if your horse comes in 1st or 2nd
SHOW bet - you collect if your horse comes in 1, 2, or 3rd
A fun/easy bet is an ACROSS THE BOARD. This is essentially 3 bets - a WIN, a PLACE and a SHOW. All three bets pay if your horse comes in first. 10 dollars across the board is a 30 dollar bet that can pay 300 bucks or much much more depending on the odds of your horse.
EXOTICS
EXACTA - pick the 1st and second horse in the race, in order. a BOX is essentially two exacta bets but the horses are reversed
TRIFECTA - pick the 1, 2, 3rd horse in the race, in order. a BOX is essentially 6 trifecta bets but the horses cover every combination of 1st, 2, 3rd.
SUPERFECTA - pick 1, 2, 3, 4th horse in the race. BOX is essentially 12 different bets with all combinations of those 4 horses.
That should get your started. The daily racing form will have TONs of info for you. There's other more complicated bets, but that will get you started. A tip for that race -
big brown is going to take all the money in the betting pools so maybe have some bets without him to try to win some real money, but you can't leave him out of a good portion of your bets
An across the board bet on one or two horses with good odds is nice
A 3 way exacta box (6 times bet) is a decent way to make some money
Trifectas can pay anywhere from 500 to 5000+ on a two dollar bet