IMPORTANT UPDATE: Part of this article has been corrected due to the Magic 2014 rules update. Please ignore the struck-through portion and refer to the updated information below.
In constructed events, you submit a deck that must be at least 60 cards and can be more. However your sideboard must be either zero or 15 cards. You are not allowed to have a sideboard of any other size. The reason for this is so it is easier to check what is legitimately in and not in a sideboard. We don’t want players to submit a sideboard of less than 15 cards and then later ‘decide’ that they made an error and add cards once the event has started.
In-between games in a constructed match, players can substitute cards from their sideboard with cards in their decks on a one for one basis. In other words, for each card from their sideboard that they add they must remove a card from their deck. You cannot either remove more cards that you put in or add cards without removing others.
As of the release of Magic 2014, neither of those things are true. A Constructed player may have anywhere between 0 and 15 cards in his sideboard, rather than 0 OR 15. In addition, sideboarding no longer must be done on a 1:1 basis; a player may sideboard however they please, so long as their deck is at least 60 cards and their sideboard is no greater than 15. A player could side 3 cards in, but only take 2 out. They could side 3 cards out of a 61 card deck, but only put 2 in from the sideboard. They could put all of their sideboard cards in and take no cards out. All of these are now legal options, as of the release of Magic 2014.
This is different in limited events. All cards from your limited pool (either a sealed pool or cards that you drafted) that are not in your main deck are considered part of your sideboard. The number of cards in a limited sideboard can vary, as the number of cards that you use from your pool in your deck can vary. This is because a limited must have at least 40 cards, but can be more if you want. Additionally, you are considered to have an unlimited number of basic lands in your sideboard for limited events. When using your sideboard in-between games in a match you can remove any number of cards from the main deck and add any number of cards from your sideboard as long as you end up presenting a deck of at least 40 cards. For example, you can take out three cards and put four cards in.