I started learning Emacs and I hope to document my learning process. So I'll try to edit this answer accordingly

Learning Emacs

This answer is two-part. This part is how to get yourself acquinted with Emacs.

Mental Notes

Make mental notes on the following Emacs-lingo and oddities:

1. C-x means press and hold Control followed press x. M-x is the same for Meta. Same goes for other keys than x.
2. Your Meta key is either Option (⌥), Alt, Command (⌘), Esc, Menu or something entirely different.
3. Esc as Meta is not a good idea, unless you don't have other options. (Mac Users, see below)
4. C-x k is not the same as C-x C-k. Same goes for other keys than x and k (obviously).
5. In a "Unix" environmont, a vanilla (i.e. your) emacs configuration is at ~/.emacs.d/init.el - .el means the file is emacs lisp.
6. Remember C-_ or C-x u - This is Undo and will help you a lot if you fuck up something.
7. Remember C-g. This cancels any command you might be in the process of (involuntarily) enter - Except when you do something like M-x. Then press Esc 3 times in a row.

You should now be ready to start acquiring your Emacs skills.

Your first steps in Emacs

1. Start Emacs and press C-h t to invoke the tutorial. Remember note no. 4 above.
2. Do as the tutorial says. You might want to follow this tutorial a number of times to start getting the muscle memory right.
3. Read 10 Specific Ways to Improve Your Productivity With Emacs by Steve Yegge - don't get offended by his douchebaggery. His suggestions are solid even though you might not share his opinions.
4. Apply desired suggestions in the above blog post to your habits and configuration file.
5. Read the answer that jlouis wrote. You might want to skip some of it steps. :-)

You're now on your way to master Emacs.

Hints and tips

This part of the answer is a list of tips, hints, tricks and what not that I and others have found helpful in our learning process.

Suggestions for Mac users

I'm using Emacs.app from macports. In order to have Emacs working "seamlessly" (non-interfering) in my Mac OS X Lion environment, I've compiled a list of my settings. I hope to extend this list as I find and fix more annoyances - YMMV:

• Have a usable working Meta key

I don't want my Command key (⌘) getting taken over by Emacs, so I've opted to use Alt/Option (⌥) as Meta. But this is potentially problematic, as Mac OS X use option as a modifier for accessing special characters when inputting text.

By issuing M-x customize-variable (use Esc for Meta if in doubt, end with return), you can change the mapping of your option key by typing in ns-option-modifier or ns-right-option-modifier. I've chosen Meta from the dropdown Value Menu for right-option, and no modifier for option, so that I can still use right option as Mac OS X option default.

On danish keyboards, you use shift+alt+7 to input \. If you map ns-option-modifier as Meta and ns-right-option-modifier as no modifier, you won't be able to input \ like this, therefore use the configuration above

• Make Caps Lock act as Control

This is a system wide remapping, but I rarely use Caps Lock anyway

From System Preferences, chose Keyboard preference pane. Under the Keyboard tab, press Modifier Keys and select Control as the action for Caps Lock.