Mistakes a beginner should avoid in Magic the Gathering with more than 2 players
Don't expect the game to end quickly.
In a MtG duel, there is a deck archetype called Aggro. Aggro decks use extremely low converted mana cost (CMC) cards that can efficiently deal damage to quickly reduce their opponents life from 20 to 0. This type of deck is trying to gain a tempo advantage. Aggro decks typically don't win in multiplayer free for all, because although they can quickly deal 20 damage against a single opponent before they can mount a defense, it is quite difficult to deal 40 (60, 80) damage to two (three, four) or more opponents. Duel decks need to deal with Aggro decks, so nearly all their card's have mana costs under 4, but multiplayer decks can afford to run higher CMC cards with bigger effects.

Don't pack your deck with cards that trade 1 to 1
In a duel, if you cast a card that destroys one of your opponents cards, you have a net card advantage of 0. In multiplayer on the other hand, you have a net card advantage of 0 with respect to one opponent, but you (and the opponent whose card you destroyed) are both down 1 card to the other players. When one of your cards destroys multiple cards of your opponents, you gain card advantage. In multiplayer though, the number of cards your single card must destroy grows with the number of opponents. This is because, for each card you draw on your turn, each opponent that is still alive draws a card. If your opponents believe you will win, expect that most of the cards they are drawing will be directed at you and your resources.

Learn the Animal Elements
Multiplayer decks use cards that excel in these areas impact (Gorilla), outlast (Cockroach), warning away (Rattlesnake), feeding-off (Pigeon), trapping (Spider), and helping others (Plankton). Anthony Alongi came up with the animals to make it easier to remember the concepts of what the cards do. Gorilla cards smash your opponents. They destroy boards, hands, and life totals. This typically means sweeper cards that effect multiple cards or players. Cockroach cards outlast your opponents cards. They cards tend to be reusable effects, are difficult to get rid of, or come back from the graveyard. Rattlesnakes warn your opponents to focus their attention elsewhere or suffer the consequences. These cards are usually permanents with no or low activation costs, whose power usually derives from not having to use them. Pigeon cards feed of of multiple opponents. These cards typically have words like, "each opponent", or "whenever [situation]" where [situation] is a lot more common because there are more players, creature, lands, etc. in multiplayer. Spider cards trap your opponents into making bad decisions. These cards are typically instants, because it is difficult to trick your opponents with cards that they can see in a visible zone. Plankton cards are all about sharing the fun. These cards allow your opponents to use them.

Concerning playing strategy
This is typically more important for larger multiplayer games than 3 player, because with more opponents there are fewer targets. You usually don't want to get into a feud with a single player. Don't attack someone, just because they attacked you last turn. Attack someone, because they are the biggest threat to winning the game. If your group allows table talk, freely explain why you are attacking someone or destroying some permanent. Helping everyone get better at threat assessment will make for better games.

Don't be an easy target
Sometimes players might get out an early aggressive creature (or several). Make sure your deck can survive early damage from aggressive decks. If your deck starts its mana curve to high (everything is 4 mana or higher), you probably can't survive even a couple of early creatures cast by your opponents.

The number combat steps steps you must survive is greater
In a duel, there is only one turn in which your opponent gets to untap and attack you or try to destroy your creatures. In multiplayer, you have to survive multiple combat steps, and your creatures have to survive multiple turns. 

Life total is an important resource
Only the last point of life matters in Multiplayer, but how close your life total is to 0 controls how aggressive you can be. Unlike a duel, where gaining life doesn't put you any closer to victory, in multiplayer when you gain life you just might make other opponents easier targets for elimination, putting you closer to victory.