Unless you're dedicated to going it alone, you're going to be earning most of your experience points while partying with other players. A typical party consists of six people and has one tank, two damage dealers, a ranged or magical damage dealer, a healer and a support member.
While this is the very definition of a "balanced" party, there are tons of variations that may be even better, depending on the situation. While Final Fantasy XI players are notoriously rigid about their party make-ups, as long as you have a tank, you'll be fine. Don't waste time waiting around for the ideal party. Some experience points are always better than none.
When partying, typically players find a safe spot to set up "camp," and it's up to one player to attack monsters and lure them back to the camp.
As noted above, a tank (or shield) is a player that holds the monster's attention so the other players can go nuts. Paladins and Ninja are the most popular tanks, but early in the game Warriors, Monks and Samurai can make serviceable tanks in a pinch.
The term "damage dealer" typically only refers to front-line fighting jobs, but can also include Rangers, Black Mages and Summoners. Most parties have at least two damage dealers smacking enemies around, in order to set up Skillchains for a mage, but more can work very well as long as they can manage Enmity effectively.
Mages fill a variety of roles in a party, from dealing damage to healing to supporting other players. The one thing all mages have in common is magic points, and the need to keep a healthy stock of them at all times. This usually means resting while the other players fight, and getting up at the right time to cast a crucial spell.
Support and Weakening
Support classes can be mages or front-line attackers, depending on what jobs you're talking about. The role of support characters is to make the party go as smoothly as possible, by weakening or "debuffing" monsters, strengthening or "buffing" other players, or speeding the rate at which the mages regain their magic points.
A puller, often called a "Fisherman" by the Japanese players you're likely to encounter, is tasked with luring monsters to the party for them to attack. Typically these are players with ranged attacks, like Rangers, Thieves, Samurai or even Warriors.