ahh.. I see.
Well "it depends"..
I'm not sure what LED you want to use..(where?.. nor how many?)
but possibly just the '1' red led? (from looking at the pic)
Most red accent leds run off of +1.7-+2.1 volts.. and need roughly 20mA at full brightness.
What resistor value you need to use depends on the battery source *(and of course the leds specs..but we'll use whats note above)
Use the led resistor calculator found here:
http://led.linear1.org/1led.wiz
you can enter in the details of the components you wish to use.
ie:
Supply Voltage: (batter source) +3.0 volts (assuming 2 x AA batteries)
Diode Forward Voltage: (voltage required for your led of choice).. for this I just use +2.0v assuming red and between +1.7v - +2.1v)
Diode Forward Current: (mA) (the current the led needs to light up nice and bright) 20mA
Calculator says you need roughly 56 Ohms of resistance.. (ie: 56Ohm 1/8watt resistor)
So:
battery (2 x AA)
switch
wires
red accent led (roughly +2.0v/20mA specs)
1 x 56 Ohm resistor
If you want to do more advanced.. I can help but you have some reading and homework ahead of you! lol