Something I have wondered about recently, is with the number of people trying out their hand at electronics (a good thing), but with little to no knowledge, is whether a "try and see" approach is a good thing?
I suppose as long as they are playing in the low-voltage, low-amperage realm, everything would be alright, but even here a lot of expensive mistakes could be made - hook something up wrong expecting a certain result, and your Arduino board could easily go up in smoke!
Really, a better way to go about learning is to start with the basics; get a cheap multimeter, soldering iron and solder, breadboard, and a collection of parts (leds, resistors, switches, transistors, diodes, etc) and maybe some simple logic ICs (old 74xx series TTL logic would be best), plus a book or two (some of the old Forrest M. Mims booklets are ideal; Grob's Basic Electronics is a great book, too), would seem to be a better (and cheaper) way to start out. If you fry a few components (or blow up a cap or two!), no big deal, you aren't out much.
I would think going this route would lead to better results (ie; this is a resistor, here is how to read the value, here is how a resistor works and what it does, here is how parallel vs. serial resistors work, etc), and less frustration...
Maybe I am smoking crack; this is just how I remember learning electronics when I went to a tech school in Phoenix, Arizona (HTI) - our first thing was to learn about resistors; our first project was putting together an analog multimeter kit from Radio Shack (while learning how to read an analog multimeter - digital ones existed at that time, 19+ years ago, but they tended to be expensive, plus knowing how to read an analog one gave you a better feel for how things worked; plus there are certain times when an analog meter is better to use than a digital one). I still have that meter, and it still works perfectly (but I tend to use a digital one today). From there, we progressed to capacitors, then to transistors, transformers, diodes, etc, culminating in building a AM radio (and all the theory and practice behind RF and other radio tech - let's just say RF is magic, and leave it at that!).
Then we moved on into the digital realm (interfacing to both IBM PCs and Amiga 500s!)...
Anyhow - to answer the poster's original question: stock up on the books as well. Find copies of both Grob's "Basic Electronics" as well as Forrest M. Mims III's "Engineer's Mini Notebooks"; Basic Electronics is pretty heavy on the theory side of things, and shows how the math behind the components works (so you can figure out things like "what is the proper bias resistor size needed for this transistor when the CE current is X"); it is a textbook, so it might be expensive for a recent edition - I doubt much has changed in 20 years, though for basic electronics needs, so find an older copy cheaper; it will be worth it, even if you don't understand it completely at first (hopefully your math skills are ok).
The Mims Notebook series is great for the practical side of things; lots of wonderful circuits to try out, and you can use them (plus Grob's Basic Electronics) to get your head around reading a schematic and visualizing part layouts and how circuits fit together and work.
Trust me when I say a sizeable library (and thank goodness for the internet!) is a valuable thing to have when it comes to electronics (oh, you might also wish to subscribe to Nuts and Volts as well as Servo magazines, if you have the means)...