What are the basics I need to know to power LEDs with RF at a range of 30 feet?
It feels intuitively like this might be possible. If you carried a 10 watt omnidirectional light bulb, in a dark place, it would certainly light up a white object at 30 ft. So why not at RF?
RF spreads out the same as visible light. The capture area of a dipole is about 0.1*wavelength^2.
So I calculate that at 145 MHz, a 5 W transmitter will deliver 5 mW to a dipole antenna 10 m away. The trick would be rectifying the RF without wasting too much of it. If you manage 50% efficiency that will produce 1 mA in the LED, which should be visible.
5 W is easily available from a handheld radio, but you'd need a decent antenna, not the rubber duck it ships with. VHF (136-174 MHz) is a reasonable choice of frequency, (you'd need a license to transmit). SMD LEDs are bright enough at 1 mA. So the hard parts are the rectifier, and getting the voltage high enough to drive the LED. A full-wave dipole has a high impedance, which might generate enough voltage (5 mW into 1000 Ohms is just over 2 V).
The finished path-light would be a string of wire perhaps 1m long, with a epoxy coated circuit in the middle. LED, diode and matching circuit. You could hang them from the trees.