Few have attempted this. A quick Google on "induction furnace" would give you the impression it's purely an industrial persuit in the megawatt range! Indeed, probably the cheapest unit you'll find is around $10,000. To date I haven't seen ONE functional purpose-built ameteur made induction heating unit. The closest anyone has come seems to be PowerLabs - a successful, though inefficient and massively RFI emitting setup. Dan has lots of information and looks to be halfway there but hasn't updated his page in years..
You know how transformers work, right? Voltage in, voltage out... Well what happens when you short the winding? Gets hot right? By George, you've just discovered induction heating. Not much use (channel induction furnaces aside), so let's open up the coil. Say, solenoid. Switch to air core (so we can fit the work in it instead) and higher frequency (so we don't need a massive air core coil) and you're pretty much there. But coupling rears its ugly head: you no longer get 1 volt/turn in, 1 volt/turn out. So you need a lot of voltage on the coil to get any power in the work. But it also doesn't need much - at least at the power level on this page - I was suprised to see it works much better with 12 turns instead of 6; and most online examples have far fewer than that!
This is my simple circuit: a 2SC3519 on stilts on a breadboard, a few support components and The Coil© (wound on an empty solder spool). Didn't get a pic of the scope trace but it's just a 50kHz sine wave with peak amplitude convieniently equal to supply voltage (minus saturation voltage, that is), a little junk at the bottom when the transistor switches and AM-style ripple on top. Fully self-excited class C operation: self-adjusting to match the load (often a load, particularly iron, will reduce the resonant frequency). The one turn pickup winding can be a piece of wire running loosely around the coil, or maybe one loop (aka two turns) if you need more drive.
Mind the parts - the coil needs to be of heavy wire (drive winding doesn't matter) and the resonant capacitor has to be rated for high current. A later test used 2.2uH at 110kHz and 25Vrms - that's 16 amperes between the cap and coil!
So how does it do?
Now this is a REALLY, really bad photograph. Apparently this room is so damned dark that the camera (not the bad camera, mind you) picks up about 3 bits of intensity information. And I always figured my room was brighter than the foundry area at night! (I've taken some dark pics there and they came out fine.) Oh well. I'll try to explain anyway: the thick black line coming from the left is a coathanger. The four smaller lines are leads for the coil and pickup winding (two turns here to account for the 20T coil). So what's that bright spot in the middle? Incandescence! :D To be exact, it was about 1400°F, near (though not quite at) the curie point.
Other things I've heated: transformer laminations (1" and 1/2" wide), steel washers, pennies, aluminum heatsink, popcan (the last three don't work too well, probably too conductive), tube shields (these work well), tubes (6AU6, 12AU7, etc.), and anything else that fits inside the coil while being conductive. The coathanger is all I've managed to heat red hot though.
The nice thing about induction is it exactly follows the laws of electromagnetism, so with some computing you can come up with coil geometries to evenly and quickly (or if the case, slowly or unevenly) heat just about any shape. Some good examples here.
And that's it. Next time -- increased output power. Or, since I can't get any more power out of this dinky supply (it's only 50W - maybe 75 if I punish it), I'll try the same things with tubes. Start with a 6BG6 then gradually move up to a pair of 4CX250R's... :D