Place bet: You bet on a horse that you think will be well placed - the exact position that you require depends on the number of horses that run in the race. The Tote rules in the UK specify that places are paid out for horses finishing 1st or 2nd in races where there are 5-7 runners; 1st, 2nd or 3rd place where there are 8-15 runners; 1st, 2nd, 3rd or 4th where there are 16 or more runners.
The odds that you will receive will usually be one-third or a quarter of the odds offered for picking a winner.

Each way bet: You bet that your horse will win OR be placed (as above). This is effectively 2 bets and you will pay twice the stake. Odds will vary.

Dual Forecast bet: You select the horses that you believe will finish first and second, in either order. Bookmakers will provide specific odds for these types of bets.