Prestige classes offer a new form of multiclassing. Unlike the basic classes, characters must meet requirements before they can take their first level of prestige class. The rules for level advancement apply to this system, meaning the first step of advancement is always choosing a class. If a charac does not meet the requirements for a prestige class before that first step, that character cannot take the first level of that prestige class.
Prestige classes are purely optional and always under the purview of the DM. The Dungeon Master's Guide encouranges all DMs to to tightly limit the prestige classes available in your campaign. The example prestige classes are certainly not all encompassing or definitive. They might not even be appropriate for the campaign in question. The best prestige classes for a campaign are the ones the DM tailors himself