First, follow these instructions on how to Integrating cocos2d API reference into XCode. This will give you a convenient way of browsing the docs, and you can also see which subclasses a certain class (like Action, say) has. Very useful.
The basic classes you must get to know are:
Director -- The class that creates the OpenGL context and manages the game's timers. This is the class that controls everything else. You don't have to know it inside and out, but just learn how to tell it to transition between scenes and a few things like that. There is one Director for the whole game, so similarly to Cocoa, you get it by calling [Director sharedDirector] .
CocosNode -- Virtually all the screen objects you will be using in cocos2d are nodes or inherit from CocosNode. You build up scenes by creating hierarchies of nodes, similarly to how you out UIViews within other UIViews.
Sprite -- The fastest way to put something on the screen is by creating a sprite (which is a subclass of node) with a file:
Sprite * background = [Sprite spriteWithFile:@"beautiful_picture.png"];
background.anchorPoint = CGPointZero;
[someNode addChild:background];
Animation -- used to create animations from a collection of frames. Sprites carry with them any number of animations which you can run at different times.
Action -- You need an Action to play an animation, and Actions are also used for things like moving the sprite around on the screen, making them bounce, flip, fade, or whatnot.
Transition -- Use this to make fancy transitions between scenes. A simple example:
[[Director sharedDirector] replaceScene:[SlideInLTransition transitionWithDuration:1.0f scene:[SomeSceneClass scene]]];
Once you've gotten this far, you should get comfortable with AtlasSpriteManager and AtlasSprite, as you should always prefer AtlasSprites to normal Sprites (for huge performance gains).
I hope that helps somewhat. Make sure to install the project templates (run ./install_template.sh from the cocos2d root folder), then just create a new project using the template and study the code. It's really very easy to get started.
NB: Cocos2D-iPhone 0.9 is now in beta, and apart from adding several nice features, all the classes will be renamed. Most of them simply are prefixed with "CC" (Sprite --> CCSprite) but some have completely new names (AtlasSpriteManager --> CCSpriteSheet).