What does over/under mean?
The over/under is a bet on the combined score of both teams. The book posts a number, called the total, and you bet whether the final score adds up to more or less than it. Who wins the game doesn't matter.
An example
A football game has a total of 45.5. If it ends 27 to 20, that is 47 points and the over wins. If it ends 24 to 17, that is 41 points and the under wins. Both sides are usually priced at -110: you risk $110 to win $100 whichever one you take.
Half points and pushes
The half point is there so the bet can't tie. Make the total 45 and a 24 to 21 game lands right on it, which is a push, and your stake comes back.
A whole number and a half number are different bets. Over 45 and over 45.5 lose on the same scores except one, and on that one the first gets its money back.
What counts
At most books overtime counts toward a full-game total. Check the rule for a game that is cut short, because in baseball, totals usually need the full game to stand.
The same kind of bet is offered on smaller pieces: a half, a quarter, one team's points, one player's yards. The player version is a prop bet.
Why the number moves
A total reacts to the things that change scoring: a quarterback ruled out, the wind getting up, a starting pitcher scratched. It reacts to money too.
Recreational players lean to the over, because cheering for points is more fun than cheering for punts, and the books know it as well as they know anything, so the price on a popular over can reflect it. I'd look hardest at the under in a game everybody is excited about. That is where the public has done the book's work for it.
Getting the best of it
I'd shop the number before anything else. A total of 45.5 at one book and 46.5 at another is worth more than any small difference in price. Then read the price as well, since over 45.5 at -120 is a more expensive bet than over 45.5 at -110. And I'd bet it the size you would bet a side, because a total is not a lesser bet and it should not be a throw-in.
The totals guide goes into how the number is made. You don't need a team to bet a total, only an opinion on the score.
Related questions
What does the spread mean in betting?
The spread is a head start the book gives the underdog to make the game an even bet. A team at -7 has to win by more than 7 for a bet on it to win. A team at +7 wins the bet if it wins the game or loses by fewer than 7.
What is a prop bet?
A prop bet, short for proposition bet, is a bet on something that happens inside a game other than the final result. Whether a quarterback throws for more than 249.5 yards is a prop. So is which team scores first.
How does sports betting work?
Sports betting is putting money on the result of a game at a price a bookmaker sets. If you are right the book pays you at that price. If you are wrong it keeps your stake. The price is built so the book earns a little whichever way the game goes.