The Help Page is fairly comprehensive about it–there’s a lot.
In any case, the basics: jobs are divided into four categories, determined by which crystal gives you each job. The Wind jobs are the very first ones you get (and also the most basic jobs, i.e. Knight, Monk, White Mage, Black Mage, Blue Mage, and Thief), and then eventually you get Water (e.g. Summoner, Berserker), Fire (e.g.: Ninja, Ranger) and Earth jobs (e.g.: Dancer, Chemist), in that order.
In a basic, no-frills-run, you’re assigned one job per crystal, so for example, you won’t get White Mage and Knight, or Dancer and Chemist; if you’re really unlucky, you might get Thief/Berserker/Ranger/Dancer. This run is also the one that most similar to regular play, since you’ll start using jobs as soon as you get them, about forty minutes into the game.
The other runs, though, play around with this. The Meteor run, for example, assigns you jobs randomly from any of the four sets, which means that your Wind Crystal Job–the one you’d start with as soon as jobs open up, around forty minutes into the game–could be from one of the other sets. In my case, my first job is Bard–a Fire Crystal job–which means that my entire party will have to be unemployed until I get to the Fire Crystal, about six hours in.
(This is not as big a hindrance as it might seem, as unemployed characters can use any and all equipment.)
Then there’s also restrictions, which affect what sort of jobs you can get or what you can do with them. For example, you can choose to play using only magic-based jobs, or to restrict each job to a single character. In my case, I have the Upgrade Jobs restriction, which on one hand means I get to choose when I begin a job (in a regular run, you have to use a job as soon as you get it), but it also means every character has to have the same job, and you can’t go back to an old job, once you’ve changed it.