This is just my advice, and is actually a very nebulous thing to answer. I'll tell you what has worked for me over the years. I'm just breaking the surface, and still learning from my own advice.
My (sage?) Advice
* Read all you can find! - the Internets have exploded with all sorts of information on electronics projects, kits, you name it. I'll have some stuff in the reading/websites section below with some specifics
* Find a mentor - One locally is great and is also a way to meet new people and get ideas. Consider your local 2600/Defcon/Maker group. At a minimum, stop in on the local HAM radio club. For what it was worth, my mentors ended up being my Dad, who was an EE and my grandfather who was a swamp yankee/inventor.
* Take something apart - Now certainly you might not want to take apart that nice $3000 flat panel TV, but find something appropriate. Check yard sales for cheap electronics, or even on trash day. For beginners, stay away from TVs and Microwave ovens (when you get some smarts they are full of good parts...). Don't discount kids toys; they can take you down the road of circuit bending! With these scenarios you won't feel bad if you break something that was broken, cheap or free. Explore! You own the hardware! Figure out what all those unknown little bits do by looking up spec sheets on the internet.
* Think of ways to make something better - You know all that crap, I mean valuable electronics, you just picked up? If something works, how would one of them be made better or how could it be made to do something else? For example, we picked up a "baby boom box" at a yard sale for a quarter. My daughter LOVES it, but it is loud, and doesn't have an off switch. See? Take it apart and add a (baby proof) switch to disconnect the positive battery lead, and add a potentiometer (variable resistor; sort of like a dimmer switch) in line with the positive speaker wire. When she's done with it in a few years, take another look at how you could have improved that design; instead of the potentiometer what about replacing an output resistor. This can get even more fun, as you can start circuit bending!
* Mind your voltages - ...and of course your positives and negatives. Don't swap them, and don't over power them (unless you read all about those power regulation chips). Making these mistakes is a great way to let the magic smoke out of your electronics. Double (even triple) check your wiring. With higher voltages (such as direct mains power), they can easily let the magic smoke out of you. Start small.
* Don't be afraid to follow in the footsteps of others - Read someone else's projects and recreate them, or in many lucky cases, build them from a kit. It is a great way to learn how to solder/desolder and learn the principles and about the parts. Learn from someone else's experience and mistakes and even improve on the design. Eventually your path will drift, and you'll be on your own road, even if it is just a slight deviation at first. Modify your kit!
* Learn to solder - Yeah, you had to figure that was coming. Also, learn to de-solder. Use all of those valuable electronics you picked up to practice both; you aren't learning on your project this way. Practice makes perfect! Yes, re-solder the pieces you just practiced removing. When you are done, you can even be left with a bunch of parts to use in another project, that are often worth more apart then the sum of the free/cheap whole. A great way to build an inventory of bits and wire.
* Start with the basics - Learn basic electronic principles; completing a circuit, switches, etc. Even though they are old, don't hesitate to use analog devices like 555 timers, transistors, capacitors, resistors and so on. Venture into microcontrollers such as Arudino and PICs as you get more comfortable. Learn how to read schematics - even the basics will take you along way.
You'll need a few things to get started of course. Start small. Go ahead and buy just what you need to work on your first project. See if you can borrow some from a friend (but return them!) for a bit. Certainly, try out the moderately priced soldering iron from Radio Shack to get started...
Here's what I find is most helpful:
* A multi-meter - I don't know how I missed this on the podcast, but this one is a must. Even a cheap digital one would be good. My Grandfather would suggest going analog to start in order to learn the basics and the tool itself.
* Dremel with grinding and cutoff wheels
* Drill press and bits, in a pinch, a hand drill (electric or otherwise) will work.
* Soldering station - I like Weller, but I have a generic. Variable temperature is best. Note, don't file down new, modern tips. They are caoted and filing ruins them.
* De-soldering iron. A "solder sucker" is Ok, but tends to be frustrating. De-soldering wick is good too.
* Small screwdrivers, jewelers screwdrivers, torx, and any other security screw bits. It is all about having the right tool for the job. This coming from a guy who just upgraded the hard drive in his MacBook Pro with a jewelers flat head screwdriver for phillips screws, and a filed down jewelers flat head to remove #25 Torx screws.
* Set of small metal files (for sharpening your cheap soldering iron, and filing down flathead screwdrivers.)
* A pair of "extra hands". A magnifying glass or head mounted loupe (both in conjunction with a good light source) is also a huge plus.
* Pliers and wire cutters are also a great idea. As are a pair of wire strippers (your teeth get tired after a while).
There is tons of info out there. Here are some of the places I learn and take inspiration from:
* Make - This is the mecca of all things hack. A little of everything, and they've really blown the doors off this thing for the whole community, making this info and reporting available for everyone.
* Hackaday - A daily dose of hacking goodness on all sorts of topics. Good brain food and they've recently started a series about all the piece parts.
* LadyAda - Limor Fried's website. Kits (at AdaFruit Industries), and general blog about electronics goodies.
* Citizen Engineer - A new video series on hardware hacking how-tos
* Nuts and Volts Magazine - Pure electronics projects that you can adapt the concepts to your own projects.
* Instructables - All sorts of step by step tutorials on all types of hacks, crafts and electronics.