I started just over a year ago with the starter kit that they provide here and was an absolute beginner just as yourself. I went in to this with only the knowledge of my freshman year physics class. The kit provides you with all of the basic electronic components, an Arduino UNO and even a book. Their book has great illustrations, which as a visual learner, were great! Though, if you get this kit you will no doubt be looking some things up on the internet, in fact it's guaranteed. As a beginner, I found the electronic component overviews by Makezine's Collin Cunningham to be very helpful. They're about as beginner as you can get. Here is one on Transistors:
Everytime the book introduces you to a new component, you should watch mazezine's description of the specific component as you do the project, to help reinforce your newly learned information.
And because Arduino's are project based, the only way you will improve is by doing lots and lots of projects!
this book I found to be pretty useful.
Also, I would take the effort to make this led resistor calculator from EvilMadScientist.com:
Its great to have a physical calculator around to have in your wallet, never know when it might come in handy! There are also plenty of online calculators a google search a way.
Eventually, once you move past the beginners kit and into creating your own projects, knowing how to solder is a must! Instructables is another great resource for beginners. Bellow is a link to a guide on soldering.
Hope this helps!