NDB - Non-directional beacon. This is a ground-based transmitter like a VOR, but just transmits in all directions. It's either a radio mast or a 'T' arial slung between two masts. It also transmits a morse Identifier, so you know you've got the right one
ADF - Automatic direction finder. Fitted in the aeroplane, and has a needle that indicates the direction from which the signals of a selected NDB are being received. Also known as a Relative Bearing Indicator (RBI). A more sophisticated version is the Radio Magnetic Indicator (RMI).
The ADF/NDB combination is, I think, the simplest radio nav. combination.
To use them in flight, you just tune the ADF to a given NDB frequency. They're used in conjunction with the heading indicator to track to or from an NDB and to fix the aircraft's position.