The best strategy you can use: ask me what I'd do, then do the opposite.
I started with a $20 bankroll, and bought a $4 copy of the Daily Racing Form. I started wagering in the third race, betting $2 on a 5:1 shot to show (meaning he ends 1st, 2nd, or 3rd). The pre-race favorite was scratched, meaning no horse in the race had ever raced before. "Apache Joe" was one of the top three favorites. His sire had gone 4-for-5, and had raced (and lost) at the Kentucky Derby. No such luck. He didn't show. He placed dead last.
In the next race, I bet $2 each on the two favorites to win. Neither one did. One of them didn't even show.
In the fifth race, I be $2 on the favorite to place (1st or 2nd), and $2 each on the next two favorites to show. The favorite came in third after tripping out of the gate, but one of the "show" bets came in first, so instead of being down $6 on this race, I was only down $3.80.
In the sixth, looking for a sure thing, I bet $2 on the favorite to show. He didn't.
The crowd favorite was a very late scratch in the seventh race, and hoping for a big score, I put $2 on a long shot, because although the morning line had him at 6:1, the betting pushed him down to 34:1. He ended 8th out of 10.
Finally, in the eighth race, I bet $2 on the horse the Racing Form said was a "best bet" and "center square and top pick". He lost. I also bet $2 each on the morning odds leader (won $3.60), and on the late odds leader (who lost).
In the end, counting the $4 newspaper, I left $20.20 lighter. Fun times, though.