Thank you very much.
This leads to another question:
If I start as fighter and multi class to mage, does it mean the DM says: "OK, you go to a temple and train there for 3 years." In the meantime the other single class characters continue the adventure, gain many levels and maybe even finish the whole story.
As I love quoting it:
The DM
may restrict the choices available based on the way he or she handles
classes, skills, experience, and training. For instance, the character
may need to find a tutor to teach him or her the ways of the new
class. Additionally, the DM may require the player to declare what
class the character is “working on” before he or she makes the jump
to the next level, so the character has time to practice new skills.
Literally everything depends on the DM who can adapt anything they want, so saying most DMs ignoring it is meaningless, but technically the character is going through some sort of training to be able to get it. However, this training isn't as intense as the initial training.
Picking up a new class is not exactly the same as starting a character
in that class. Some of the benefits a 1st-level character gains
(such as four times the usual number of skill points) represent the
advantage of training while the character was young and fresh, with
lots of time to practice. When picking up a new class, a character
does not receive the following starting bonuses given to characters
who begin their careers in that class:
Maximum hit points from the first Hit Die.
Quadruple the per-level skill points.
Starting equipment.
Starting gold.
