The horse that crosses the finish line first is the horse that wins (barring any objection of foul that may change the order).

Usually the minimum bet is $2

What to say:

Name track you want to wager first
Then add
"2 dollars to win on the number ??"

The "odds" displayed before the race are an approximate of the payout of that horse is it wins the race.
Example:  If horse #2 is displayed as a 4--it means that that horse will pay 4 dollars of winnings for every $1 of wagers.  For a minimum $2 wager you will receive $8 of winnings and your original bet back of $2 = $10 returned for winning ticket.
Example:  If horse #3 is displayed as a 7-2 -- it means that that horse will pay 7 dollars of winnings for every $2 of wagers.  For a minimum $2 wager you will receive $7 of winnings and your original bet back of $2 = $9 returned for winning ticket.

Sample odds for winning payout displayed on tote board:
1:1  you will win $1 for every $1 wagered  TOTAL $4 for a $2 bet
1:2  you will win $1 for every $2 wagered  TOTAL $3 for a $2 bet
2:1  you will win $2 for every $1 wagered  TOTAL $6 for a $2 bet
3:2  you will win $3 for every $2 wagered  TOTAL $5 for a $2 bet
1:5  you will win $1 for every $5 wagered  TOTAL $2.4 for $2 bet