The single most important piece of equipment you will need for a game of soccer is a foot. After that, the ball is important, too. There are no surprises there, since the game is football---and unlike U.S. football (in which only the lamest players do anything to a ball with their feet), it is appropriately named. The official soccer ball is made of leather, is 27 to 28 inches in circumference, and weighs 14 to 16 oz. While having a ball is more or less critical to the sport, you may want to bear in mind that Diego Maradona---arguably one of the greatest players ever---grew up in Argentina playing with a clump of rags, and that the Brazilian national team---unarguably the greatest soccer-playing country ever---often practices with tennis balls. If you really have a passion for the sport, just find something round and kick it about (except babies and puppies as they're too cute).
If you want to take things very seriously, though, you'll need another piece of equipment: a very large field. Soccer fields are similar to U.S. football fields in dimension, between 50 and 100 yards wide and between 100 and 130 yards long. At either end is a goal, threaded with a net, and on the four corners of the field are flags.
Another piece of equipment vital to the game is a coin, to be tossed and forecast as a way of initiating the game. The referee calls the two captains to the center of the field before the game begins and asks the home captain to call the coin in the air. Whoever wins the toss has the option of determining either which team kicks off or which side each team plays on. The loser is then assigned the remaining choice. It's all rather civilized--at least on the field, anyway.
Beyond the institutional equipment, each player will need to have a pair of football shoes--or cleats, as they are called in the U.S. That, of course, assumes that the game is being played on grass. If the game is on turf, the players will wear flats, which are common among non-soccer playing undergraduates. Every player is also required to wear a pair of shin guards, which are exactly what you would think: a hard plastic pad surrounded by softer fabric that extends from below the knee to above the ankle, usually secured by Velcro straps, and designed to avoid fractures to the shin, which is so vulnerable in a sport in which everyone is kicking all of the time.