Hi Derrane,
The easiest way to get started is with 4 LDR's looking at the candle at different angles - LDR = Light dependant resistors. You connect these to the analog in of the Arduino to 4 analog ports. See - http://learning.codasign.com/index.php?title=Light_Dependent_Resistors_and_Arduino -
Instead of printing the values you can put the values in a function that approximates the flickering. The output of that function is send with digitalWrite to a PWM port control a LED light. You can find this on the reference pages and tutorial sections of arduino.cc
You can also map every LDR onto its own LED, program a memory effect and add additional random fluctuations but that is for version 2.0. First get started with 0.1 understanding teh sensors and the basic program.