One of the biggest confusion points for new (and experienced!) players is what constitutes a foul ball or fair ball when it's near the line, so let's lay it out with the aid of a handy dandy chart.
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With fly balls, it's much more straightforward. The ball lands with any part in fair territory it's fair, lands fully in foul territory it's foul. Of note, the line is considered fair territory.
Now the tricky stuff: what happens when a player touches the ball in the air? The most important distinction is where the ball is when it is touched. A ball in touched in fair territory is fair, no matter where the defensive player is standing. A fair ball cannot be made foul by reaching in from foul territory. The inverse of that rule is NOT true though: a ball that is in the air in foul territory CAN BE MADE FAIR if touched by a defensive player in fair territory. Here's the exact text of the rule:
1.04 Any player or Referee wholly or partly in fair territory is an extension of fair territory. Any live base runner outside the kicking box is fair, even when wholly in foul territory. A player jumping from fair territory is in fair territory while in the air. A player in foul territory does not extend foul territory by jumping or reaching into fair territory.
This means that if you are running to make a play on a ball that is just outside the foul line and touch the ball while you are partly still in fair territory, the ball is fair even though it was in foul territory as your body extended fair territory. You can do this by jumping as well. A baserunner wholly in foul territory on the third base line could be struck by a kick and called out, and the ball would be fair and still live! Basic rule of thumb, you can't make a fair ball foul, but you CAN make a foul ball fair (so long as it hasn't already touched the ground fully in foul territory).
That's it for this week, let me know if you have a rule you'd like me to go over in the future!