The basics of sportsbetting
Forms of betting
The most common form of betting is done with fixed odds, where the accepted initial odds dictate the return. Some other perhaps less known forms of betting are:

Tote, where all the bets are pooled and the pool is shared out among the winners, minus a deduction.

Index/spread betting which a form is derived from financial markets in which bets are placed on a spread of numbers related to a particular event. Returns are calculated in proportion to how right or wrong the bettor is, and can lead to large winnings or losses.
The bet
A bet is an agreement between two parties (i.e. bookmaker and bettor) that the one who has made an incorrect prediction about an uncertain outcome will forfeit something stipulated to the other. In online betting, a bet is a pledge of money that a certain outcome will occur.
The bookmaker
The bookmaker is either a company or an individual who runs a business in taking bets from punters. Punters can use bookmakers to place fixed odds bets or alternatively use a betting exchange in which the punters bet against each other. By using a betting exchange a punter can also act as a bookmaker by offering (laying) bets to other punters with their own odds.
The odds
The term odds mean the multiplier which a successfully made bet returns money to the punter. A common disbelieve is that the odds actually represent the likelihood of the particular outcome.
What you should consider as a punter is that the bookmakers produce the odds by employed independently operating odds compilers. This brings the human factor to the odds and they can vary dramatically from person to another. Another thing to remember is that the bookmakers run a business which requires them to make profit. They achieve this by setting an overround and dropping the estimated probabilities for the outcomes to pay out less in winnings than they receive in stakes. Thus the odds you bet on are the bookmakers estimation of the chance of an outcome adjusted to include its own profit.
When a bookmaker offers odds to a market they will always take in account the amount of money staked on each outcome and then adjusted to respond the betting trends: When a lot of people bet on the same team the bookie runs a risk of losing a lot of money unless he encourages people to bet on the other side by lowering the winning favourite’s odds while pushing the underdog’s odds higher. In this light it is clear that at a certain point the odds cease to indicate the estimated outcome of a match and display the betting trend instead.
Odds formats
You might see the odds shown in three different formats although with online bookmakers you are usually able to choose your favoured format.
European style decimal format; the most common one. It shows how much money will be returned from a 1 unit (unit can be for example a Euro) stake.
Example:
Stake 100€ at 1.90
Payout 100*1.90=190€
UK style fraction format; popular with UK bookmakers. It shows how much profit will be given to a stake of 1 unit. To convert UK odds to European decimal odds you have to add 1 to the UK odds and you will get the decimal version of the odds. That is also how you will calculate payout.
Example:
Stake 100€ at 4/5
Payout 100€*(1+4/5) = 180€
American format; negative or positive odds.
The negative odds show how much money you have to stake to win 100 units. To calculate the payout you need to use the following formula: Stake*(1+100/US odds).
Example:
Stake 100€ at 125
Payout 100€*(1+100/125) = 180€
The positive odds show how much profit will be given to a stake of 100 units. The winnings are easiest to calculate with a 100€ stake. If a team is priced at +500, you will get 500€ from a stake of 100€. To calculate the payout with a different stake you need to use the following formula: Stake*(1+US odds/100).
Example:
Stake 50€ at +250
Payout 50€*(1+250/100) = 175€
Sometimes you might stumble upon an SP instead of numbered odds when betting on horse races. SP stands for Starting Price and is an exception to the fixed odds general rule. SP is an average price calculated at the start of the race by the race course officials using prices shown by oncourse bookies. This way by backing a horse you are agreeing on whatever the odds will be in the start of the race as the bookie is unable to tell the exact odds upon making the bet.