Often the key to diagnosis is correctly identifying valves. The function of valves can usually be discerned by how many and what types of tubing are attached to it. Are they all air lines? Water? Some of each? All manufacturers color-code their tubing for easy identification, one of the most common brands in the US is, A-dec. Following are the codes used by A-dec to identify their tubing.
Some of the terms used above may be confusing or unfamiliar.
"Signal" air is air that is used to turn a valve on. Signal air is provided by a relieving toggle as discussed in a previous post. Signal air is what turns the entire unit on, it's what activates water to your handpieces, it is more common than you might think.
A "Live" line is constantly pressurized as long as the unit is on. It does not require activation in any way. These are good lines to tap into if you want to add a quick disconnect to your unit or an additional air/water syringe (for example).
"Regulated" lines have their pressure precisely controlled. Most units should be set to have the regulated main air lines set to 80 psi and the main water lines to 40 psi.
The colors shown above are specific to A-dec, but many others use similar colors as well. Yellow for air and blue for water are quite common color choices, for example.