The outside bets on a roulette board are simply the bets that reside 'outside'
of the main playing area of 38 (yes, sometimes 37) numbers. There are no
winning outside bets for 0 or 00 results. This is what gives the casino
the majority of it's house edge; people love to play the outside bets because
they often seem like a 50/50 chance, when in fact they are slightly less
than a 50/50 chance.
Red or Black - You can choose to bet on the outcome either being a red number, or a black number. Place this bet right in the area with the words 'red' or 'black' in them, which should be easy to reach from beside the table. Don't fall into the classic mind trick of assuming that if 5 blacks were spun, there is a better than 50% chance the sixth spin will be red. This is not logical and the reason why is described in more detail on the roulette system page. The Red/Black bet is paid even money, meaning if you bet $5, you win $5.
Odd or Even - Similar to the Red/Black bet, this even money bet is based on whether the number will be odd or even. Since 0 does not count as either, there are 36 numbers, an even count between odd and even. Place this bet by putting your chips in the middle of the square marked 'even' or the square marked 'odd', which will usually reside on either side of the black / red betting area.
Low or high - This bet lets you predict whether you think the next number to come up will be part of the range from 1 to 18, or part of the range from 19 to 36. This is an even money bet. To place this bet put your chips in the boxes with the associated number range printed in them.
Columns - At one end of the set of 38 numbers are boxes with the words '2 to 1' written in them. Each box is part of a column of numbers (if you extend a line up the body of the inside of the betting area). If a number from within the column you are betting on comes up you win, and you're paid 2 to 1.
Dozens - a bet very similar to the columns bet, dozens lets you place a bet on either the first dozen numbers (1-12), the second dozen (13-24), or the third dozen (25-36). To place this bet find the rectangular areas located in between the first outside bets (red/black, odd/even, etc) and the inside board spread. These will usually be labeled with the words 1st 12, 2nd 12, and 3rd 12. The bet pays 2 to 1.