Honestly starting on a few C++ tutorials will help you out, as the Arduino environment uses a watered down version of it - learning how to work with integers (rounding/min/max/floats etc.) and creating objects and functions will let you not just use code example, but understand why they work and how to make them to your needs.
A cheesy intro to electronics and measurement should always be good:
http://www.noisemantra.com/Physical%20Computing/Intro%20to%20Electronics.pdf
Resistor colour codes are a pleasure once you learn them. Grab a pile of the E12 series (http://www.st-andrews.ac.uk/~www_pa/Scots_Guide/info/comp/passive/resistor/e12/e12.html) from eBay or something.
Multimeters are cheap (cheapies will do for now, have more than one) - you can even make an Arduino-DMM if you ensure the inputs are always within its allowed range (0-3.3 or 5V?) for practise using the ADC.
Some random tutorials reveal advanced contexts and tips in how others program things (try to make clean, self-explaining code, and document where the code doesn't explain itself through code comments - it'll really help.)
http://tronixstuff.com/tutorials/ (this guy took a lot of time making quality tutorials, some aren't so good.)
or where to go from Arduino and expand into scratch built electronics.
Quite easy - I bought a PICkit 3 programmer for example..so with a $2 or so 8-pin PIC12f up to a beasty PIC18f you'd just need a bit of supporting hardware such as a voltage regulator or crystal, and you can replicate your Arduino projects as finalised projects in a small form factor for under $10 (Altoids tin stuff? permanent door sensor? who knows.) - it's close to real life electronic products then, although they use tiny tiny surface mount parts now..fun..
For other components.. most are simple things with voltage ranges, output results in a predictable or standardised manner, maybe looking up some op-amp tutorials will help you learn amplifiers and buffers.
*shrugs* ask away if I didn't cover much, just an excitable tiger. :P