How can multimeter measure frequency with only one wire connected? Many multimeters have the ability to measure Frequency along with AC Voltage, DC Voltage, Capacitance, Resistance ...
But how do they measure Frequency?
In my country, $50\ \text{Hz}$ is used as AC frequency. My multimeter has a "$\text{Hz}$" option. So, I inserted the leads into the power outlet (in the phase and neutral) and turned it on. The Frequency measured was $\sim 50\ \text{Hz}$. Everything was okay until I turned off the switch and removed the neutral lead - it still measured $\sim 50\ \text{Hz}$. Then I just touched the "Red" Lead to the switch board (plastic) and it measured $\sim 50\ \text{Hz}$. 
How can it determine the frequency without touching the phase wire? My guess is that due to the changing magnetic flux (due to a change in magnetic field of AC), AC is induced in the multimeter and using that, it determines the frequency.
 A: Your guess as to how they 'hear' the 50Hz frequency is correct.  If you have fiddled with audio electronics, or played the electric guitar you will know that 'mains hum' – 50Hz (sometimes 100hz) in countries with 50Hz mains and 60Hz (sometimes 120hz) in countries with 60Hz mains – is a pervasive problem which leaks everywhere.
Occasionally hum leaks into things because of inadequacies in power-supplies: there can be 'power-supply ripple' because of inadequate smoothing. But much more often is is because there is just a lot of mains wiring around and all of this stuff is causing EM fields around it, which then induce small currents in other wires, such as the coils of guitar pickups, microphone cables &c &c.  This is a problem if the signals these wires are carrying are themselves small.
The reason the multimeter is 'hearing' the hum is because it's got long cables attached to it for the probes, it has a rather high impedence (which you want for something measuring voltage!), and it is also just rather sensitive, so it hears ambient hum.
A: inside the multimeter there is a peak-detection circuit which finds the topmost point in a sine wave that is applied to its input leads. Once it detects a peak, it starts a timer running which is shut off when the next peak in the sine wave train is detected. the meter then knows the time-between-crests of the sine wave and from that it calculates the frequency of the sine wave. 
unshielded lead wires behave like an antenna, causing the multimeter to pick up radiated electromagnetic interference  from any power lines nearby. and for auto-ranging digital meters, the meter itself will ramp up its gain until it can detect a signal, even if that signal is tiny. so the meter will read 50hz even without a direct connection to the power lines, by picking up the radiated EMI.
A: An alternative to measuring the time between peaks, would be to count the number of peaks which occur each second.  Either method would require an accurate internal clock.
