The first step in this type of circuit analysis I have found, is to attempt to simplify the circuit as much as possible. This means:
remove any jumpers in circuit
add in ground and power symbols to reduce clutter
attempt to identify common circuit elements - Utilize the manual for the device you are reverse engineering if possible. This can give clues about certain portions of the circuit.
A Non Exhaustive List of Common Circuit Elements
darlington pair, with or without base-emitter bypass resistor
