Aircraft use DME to determine their distance from a land-based transponder by sending two pulses with a random time interval between them. The transponder echoes the pulses. The DME receiver then searches for two pulses with the correct time interval between them and measures the delay between the pulse transmission and the pulse transmission.
Once the receiver is locked on, it has a narrower window in which to look for the echoes and can retain lock. A typical DME transponder can provide concurrent distance information to about 100 aircraft.
DME frequencies are paired to VOR frequencies. So generally a DME interrogator is designed to automatically tune to the corresponding frequency when the colocated VOR is selected. DME frequencies are around 1.025 to 1.150 Ghz.
One important thing to understand is that DME provides the physical distance from the aircraft to the DME transponder. This distance is often referred to as 'slant range' and depends trigonometrically upon both the altitude above the transponder and the ground distance from it.