A rectenna can be a simple dipole antenna with an RF diode at the dipole feed point. 

The diode rectifies the AC induced in the antenna by the RF, to produce DC power, which powers a load connected across the diode. Schottky diodes are usually used because they have the lowest voltage drop and highest speed and therefore have the lowest power losses due to conduction and switching.  The 1n34 germanium diodes also work but not as well as others.  Some of the Schottky diodes tried include the 1N5711, 1SS86 and1SS106.  I also had some 1N21s and 1N23s in my parts kit and they worked great.

To use a LED as the load  the rectenna diode cathode goes to the LED's anode and vice-versa.  To get maximum power transfer the dipole is resonant at the transmit RF frequency.  

 I have a couple of possible transmitters - a ham handy talky and a WiFi access point.  The 1/4 wavelength for 434 MHz works out to 6.8 inches and 2.4 GHz to 1.2 inch.  

The rectannas can be arranged full wave voltage doubler style and can be arrayed to cover a greater area to collect more energy.