It depends on the prestige class, or for that matter, the base class. As it is, here's my general take on things:
If there's someone in the party who already has the base class that a character wants to pick up a level in, then they can just do it. There's someone on hand who could be helpful, that they've been able to pick up a few things from, and it helps to keep the game flowing.
Furthermore, if a character class is a natural progression off of abilities they already have, then they can multiclass as they wish. A Ranger could readily multiclass into a Rogue or Fighter, as I see it, whereas a Barbarian might be able to readily go into a Ranger or Druid. So long as it's conceivable the character naturally flow from one class into another, that's fine. The same would go with, say, a Cleric/Wizard into a Mystic Theurge. It's just the natural progression of what they've been doing.
A number of prestige classes that are attached to groups also assume that not all, or even most, of those in the group have the prestige class. As such, if a character in one of my games is already a member of a group with a prestige class, they don't need to seek out training to pick up the prestige class. Already having been a member, and working at the prerequisites for the class, represents turning ones abilities towards refining what the prestige class will eventually offer. Besides, it doesn't make sense to try training to be, say, a Loremaster by going out and schwacking monsters. If someone wanted to be a Loremaster, they'd be training in a library or the like, not playing whack a mole in a dungeon. So I allow leeway for field training, as it were, as someone looking to enter certain prestige classes wouldn't be adventuring in the first place, and certainly wouldn't be using the logic of "If I kill some monsters for a few years, I'll eventually be able to become a better diviner." Or something crazy like that.
Anyway, short little blurb on things, there you have it, my minds currently a bit out of it, so I'll leave with just those previous words.