Rules-as-written, when you gain a level in a new class, you immediately gain all all the class benefits that a first-level character would, except that you do not gain 4x skill points, maximum hit points for your hit die, starting gold, or starting equipment.
Rules for adding a second class appear in the Player's Handbook, p.59:
As a general rule, the abilities of a multiclass character are the sum of the abilities of each of the character's classes.
The character gains the 1st-level base attack bonus, base save bonuses, class skills, weapon proficiencies, spells, other class features of the new class, hit points of the appropriate Hit Die type, and the new class's number of skill points gained at each additional level (not that number x 4, as is the case for a first-level character).
The DM can require players to undergo special training before gaining a new class, but the rules don't suggest delaying acquisition of class abilities once the level is gained:
The DM may restrict the choices available based on the way or she handles classes, skills, experience, and training. For instance, the character may need to find a tutor to teach him or her the way 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.