some basic ideas you could experiment with:
use a 555 based timer to switch current on and off into a large coil of wire (your primary)
use a second smaller coil with a rectifier, some capacitors and some sort of load, to see how much DC voltage you get
my idea is, the 555 timer switching current on and off into a coil will generate an electromagnetic field around the coil. another coil will absorb some of that energy through induction. then the rectifier and capacitors will smooth it into DC, and you can power your load with it.
of course, using something a bit less crude than a 555 timer, like a sawtooth or sinewave generator would produce better results, but a humble square wave might be enough to get you started
be sure to snub the back voltage your coils will generate when the input current is turned off