Like Gar said, an understanding of how and why things work, and what a working system "should look like" when functioning properly are a beginning to troubleshooting. Then from there taking logical steps backward to source of problems. Then knowing how to correct once you find the problem source is the final step. I've seen guys just start throwing parts at an issue then after a lot of money spent either give up or find what was really a simple problem. This not limited to the electrical field but have seen in mechanics, plumbing and appliance, any area where troubleshooting is involved.
Experience over time is a big part of simplifying your troubleshooting tasks, many issues will present in a specific fashion and your experience will point you to a fix quicker without having to rip everything apart, this part cannot be learned from a book, and is an ongoing learning curve. A good source while not comprehensive but gets into a lot of "real world" application of troubleshooting is this forum under troubleshooting. Look through that and see how the logic forms (most times lol). Another piece is the homeowner or machine operator or whomever is reporting the trouble, always lies (or leaves out key parts of the picture) so experience is key to "trying" extract needed information for troubleshooting. 90% of the time, on trouble calls will eventually at some point find something the owner deliberately or absentmindedly neglected to mention when I was first asked to look at the issue.
If you are going to be dealing with mostly specific equipment, getting the service manual (if there is one) would sometimes give a step by step trouble diagnostic methodology for that equipment. That doesn't replace basic knowledge though.
Don't know your electrical background or if you are licensed and what level, but if your prior employment didn't provide the opportunity to learn that phase of electrical work (troubleshooting) during your apprenticeship, jumping straight into a troubleshooting role will be like trial by fire. Mike holt has some good publications that go into basic electrical theory that you might be benefited by "IF" that is where you are lacking. I know of a lot of EC who get apprentices and never have them learn theory only the mechanics of the trade, and these guys will struggle with troubleshooting. Early on I work for one of those types and had to learn theory kind of backwards, learning (and still learning) after the mechanics.