For anyone just starting out with blender, I highly recommend:
Learn CG fundamental Concepts
The short videos from the Guerrilla CG Project are not specifically blender related, but teach fundamental 3D graphics concepts. They are all informative and presented very clearly and professionally. But at the very least, spend 15 minutes to watch these 4:
Print a Reference Sheet
These reference sheets help get an overview of how blender works, as well as helping to learn some of the MANY hotkeys (essential to getting fast). My favourites are #3 and #5 below, but see what suits you.
Here is a simple Blender Basics Quick Reference Sheet I created
The official Quickstart Guide hasn't been updated in a while but is still pretty good
This unofficial update to the Quickstart Guide is more current quick overview
The Key board map is kind of helpful
Blender Guru's Blender Cheat Sheet is more thorough and easier to read. It is free, but you have to sign up on his mailing list to get the download for it. Since his tutorials are excellent, his mailing list is not a bad thing to be on.
Get Started with Blender Video Tutorials
If you can't get a personal tutorial from a friend, then watch the Get Started with Blender video tutorials at CG Cookie. This a 7 part series will takes about 40 minutes to watch, but give yourself at least 10 minutes between each one to try out what you've learned.
Where To learn More
That gives you a good running start. But is a good idea to have a sense of the other great resources available so that when you get stumped you know where to look:
Blender Nation News about Blender, tutorials, CG and the industry
Blender Cookie Tutorial site
Blender Guru Tutorial site
Blender Nerd Tutorial site
blendtuts Tutorial site
blender cycles Tutorial site
The Process Diary Tutorial site
Blender Newbies Tutorial site
Blender 3D: Noob to Pro instructional wiki-book.
Introduction to Character Animation A really good (but long-ish) tutorial
Blender Materials Online material repository
Blender Education List of Tutorial Sites, demo files, forums and chats
Google it! Seriously, type in blender and the topic of your choice and check the video results first. There is lots of stuff out there.
Get Inspired!
To see some amazing stuff done with blender, have a look at:
Blender Open Movie Projects Especially worth checking out are Big Buck Bunny, and Sintel (IMHO)
The upcoming film Project London
The latest upcoming blender foundation open movie project
http://www.blender.org/features-gallery/gallery/art-gallery/