I found a great article on how to troubleshoot and repair a standard washing machine. As the article’s introduction points out rather succinctly, there are a lot of parts and pieces to a washing machine, which makes diagnosis of a particular problem difficult.
The article covers basic checks, cleaning the washer, disassembling it, checking the various parts to the machine (switches, timers, valves, the tub, agitator, belts, pulleys, and the motor), and water-related issues.
The article contains plenty of details and even the occasional picture to help you on your repair quest.
As always, make sure you take the proper precautions and unplug the machine, detach the water hoses and the grounding wire.
Good luck!