Lacrosse is a sport that evolved from the Native Americans. It was a war ritual, training for combat. The game hasn't changed much since they played back then. A ball is passed and shot with sticks that have what amounts to a basket on the end. The ball, which is also referred to as the rock, is typically made of rubber with a metal bearing in the core. Players for outdoor indoor and outdoor lacrosse wear virtually identical equipment: a helmet with full face shield, shoulder pads, rib pads, elbow pads, and gloves. Other than the optional cup, there is no lower body protection. Attack and middies use 'short sticks' during play. The length of the shaft of their sticks is shorter than the goalie or defense sticks. Defense have the longest length sticks. The goalie's stick is about halfway between a shortstick and a longpole. Here comes some differences between indoor (also called box lacrosse) and outdoor (field lacrosse). In outdoor, the field consists of 10 players. Goalie, three defense, three middies, and three attack. Indoor typically only allows short sticks, so there are five players and a goalie. The goalie has the same stick as in outdoor, but is allowed much greater padding and protection. Indoor goalies look much more like hockey goalies because of the bulk of the padding.
I'm going to focus more on outdoor, as it's the form that most highschools and colleges compete. It's also the form for international competition.
The starting lineup will take the field and line up parallel to the endlines, facing the other team. The two goalies will cross the center line, shake hands, then go to their creases. After this, opposing sides shake hands, and get set for the faceoff.
Two players crouch down with the heads of their sticks facing them. The referee will announce "Down......Set....." and then blow the whistle. The two faceoff players will then battle for the ball. During this, the attackmen and defense are restrained. They are not allowed to leave the restraining box (which is painted on the field) until the referee announces "Possession" or until the ball enters their respective zone.
At any given point, there must be three offensive players in the opposing team's defensive end and three defensive players in the opposing teams offensive end, excluding the goalie. Defense can switch with middies who can switch with attack. There's no limitations on who can go where. If a defenseman takes the ball past midfield, a middie has to stay back behind midfield so there are three "defensive" players. Otherwise this will be called offsides. If called offsides with possession, it is a penalty. If there is no possession and offsides is called, it's a turnover. Essentially, you have to have three players on one half, three on the other, and three free to roam. Again, this discounts the goalie.
Penalties are similar to hockey. Slashing, cross checking, holding, interference, etc. When an infraction occurs, play will stop immediately if the ball is not in the control of the team who will be gaining the power play. Play will continue until the ball is turned over or dropped. The typical call for a delayed penalty is "Flag down!" Man-up situations work much like a power play in soccer or hockey. The short handed team is still required to keep three players on one side and three players on the other.
Although only three defense are required to have longpoles, one additional player is allowed to use a defensive stick. During a short handed situation, this is typically a fourth defenseman. During regular play, the extra pole is referred to as a Long-stick Middie (LSM).
The goalie is protected by a 9' diameter crease. He is untouchable within the crease, and if the opposing team enters the crease it will result in a turnover. The goalie is considered "in the crease" even if only a toe is in the actual circle.
The goal is a 6x6 metal frame that has a base that comes together at a point in the rear. It is commonly referred to as "the cage" and is usually painted orange with a white net.
The field extends behind the goal and the crease, much like in ice hockey, but allowing much more room behind the net.
There is quite a bit more to lacrosse than what I've listed above, but this should give enough of a basic description of outdoor games for the casual observer to understand what's going on.