How to create a simple circuit with your body
Always be very careful when designing circuits that are ment to put a current trough your body.
It would be dangerous to let the current for the LEDs actually flow trough your body. 
What the people at the museum probably did is use some kind of amplifier. 

The resistance of a human body (including the skin) is somewhere between 10 kilo ohm and 100 kilo ohms, so with a voltage of say 9V, you could only get a maximum current of 1mA. For a normal LED a current of 20mA is needed. 

A simple type of amplifier is a darlington transistor. You could make a simple circuit as shown below. A small current that goes trough the body (shown as resistor) is amplified by say 1000 times. This would mean that to light the LED, a current of 20 micro amperes is needed, this can be considered safe.  

Another option is to use a MOSFET. MOSFETs switch on when a certain voltage is applied, so the approach is a little different. A tiny current goes trough the body and trough R4, creating a voltage on the Gate of the MOSFET, making it conduct. In this case the current trough the body is even smaller, about 1 micro ampere.







simulate this circuit &ndash; Schematic created using CircuitLab