1) Walk in and take complete charge of the situation. Ask lots of questions. Take notes on the answers. Don't be afraid to get a little bossy (not a lot bossy, just a little).
2) Resist the urge to pull out the laptop as the first step. As Ken mentions, there are a host of issues with doing this. Since it is very unlikely that the program broke, odds are it is something much more mundane. Play the odds. Using the PLC to find the issues on a machine IMHO will deaden your diagnostic skills over time. It is also a perception thing. If you fix the problem without using your PC, then they have to think "wow, we could have solved that ourselved had we just though about it". The reverse is true, if you crack your PC open, and you could have figured the problem out without it, they still see that you used your PC to solve the problem and will develop the notion that only people with PCs hooked up can find and solve their problems.
3) If management comes back and starts to pressure you for answers. Give them answers. Don't put it in laymens terms. Give it to them straight with no BS. They won't understand what you are telling them anyway and they really don't care what is wrong. They only care about two things. They need to know WHEN you will have the machine up and running, and they need to know that you are the right person for the job. Obviously, you can never give them a definite answer on "how long". Instead, give them a few scenarios and roughly how long each of those scenarios will take.
4) Always listen to and observe the operators. Make them comfortable with you. It is like a doctor / patient relationship. They know all the symptoms, and your initial diagnosis will be based on those symptoms. You have to take everything they say with a grain of salt.
5) Always check it again YOURSELF. This one point is by far the biggest trap I have fallen into in the past. When someone else says they have "checked" something, don't be afraid to say show ME. You would be suprised at how many "technicians" don't know how to properly test certain types of components. (i.e "I checked the sensor and it was working" might really mean "the little orange light on the prox still goes on and off, but I didn't actually check to make sure the signal is getting all the way back to the input card")
6) Trust what you know. If something doesn't make sense, don't let it slide.
7) Take about 10 to 20 minutes just to study the machine. Break it up into it sub-parts. Walk your mind through the entire process from start to finish so that you understand what it is doing. Isolate the subsystem that is malfuctioning. Think for a couple minutes about how you would have done the application had you never seen this machine before. This will give you an oportunity to put yourself in the shoes of the original designet, and will allow you to understand some of the subtleties of what they had to deal with. This last step is important, because you need to remove all the mystery out of your own mind about the machine.
8) Try to enjoy what you are doing. Think of yourself as the star athlete on a team that is down by a score and are relying on you to bring the championship. Critique yourself while you are working. Continuously ask yourself questions like (am i making the best use of my time, am I playing the odds correctly, am I following a logical deductive path to the answer). Make a science out of your approach. After you are finished, ask yourself how you could have done better. Frame this within your own mind such that it is an enjoyable process. If it isn't, maybe your meant to do something else.
9) When you do find the cause of the problem, explain to them what the problem was, what did or probably cause the problem, what is necessary to fix it, and what might be necessary to prevent it in the future.
10) If you find yourself being continuously being called out to the same problem over and over again, then you are likely a large portion of the problem. It is imporatant to really FIX the problem. Re-current problems usually expose poor engineering. Unless you enjoy being brought out to fix the same thing over and over again, tell them what needs to be done to fix it once and for all. Insist that they fix it this way. If they refuse, then it might be a sign that you need to move on. You can't help people who refuse to help themselves.