I look up the function of each and every IC in the datasheet, and follow the truth table. 

Then, i hook up an o-scope, 1 channel on an input, and 1 channel on an output. I basically figure out if the chip is following its truth table. If not, then its bad and has to be replaced. 

And this is the hard way. The better way is have a working board side-by-side and compare scope shots, its really easy to figure it out at that point.