Relative simple really. There is a How To Article on Radio Control Wiring on this site that gives useful advice.
You need a 3v or higher dc supply and a resistor to limit the current flow, 470 ohms to 1000 ohms at 0.25 watts will usually work. The lower the value the brighter the light.
They are polarised so will only work if connected correctly so if it doesn't work just reverse the connections. The resistor can be in either lead. No resistor usually results on destruction of the diode.
Compared to incandescent lights they are cool running when not too bright so are ideal for using with plastic fittings. They use minimal current and are available in all colours, including u/v and self flashing and from 10mm down to 2mm, plus you can also buy surface mount types about 1mm.
My RMS Olympic build blog detailed my installation of several hundred LEDs for portholes and the use of home built 317 voltage controllers. The total current was less than 200 Ma.
For a simple set up a battery and resistor works fine so should be well within the capabilities of the average modeller.