I have to agree with Jingles, mostly because he said it first.
You have to take into consideration that rental places make their money on renting gear, not being wizards with their gear. It's not surprising to me that they don't know how to program the DMX Operator. Heck, I don't know how to program mine, but I know how to operate it. Just, the programming has a very specific procedure to enter and exit programming mode. Granted, this isn't complicated, but I've just made a decision to not memorize it.
What is a scene? A scene is a "snapshot" of how you set up your controller's settings at a specific point in time. Let's say, for example, that you bought a color changing fixture. You could set it to yellow, and then save that as a scene. You could change it to red, and then save that as another scene. Scenes look at all settings, so let's say you were doing something much more complex that my examples, it's not a problem.
What is a chase? Chases rely on scenes to work. Without scenes, you can not build chases. A chase is a sequence of scenes.
Going back to what Jingles said, please DO read the manual. Why? The manual is quite well written, but at the same point, one really should work AT the controller while reviewing and applying what was described in the manual. What didn't make sense THEN will make sense now. I printed out JUST the programming pages. I can't find them right now, but since I have the PDF, I don't think that's an issue.
Also, I realize that last minute stuff happens. You do need to plan ahead. If you think you're going to need a controller all the time, Guitar Center is having a special on the DMX Operator right now for way inexpensive, so inexpensive I want them to re-hire the guy who sold me mine and smack him because of the price drop! But, another option may be something like MyDMX, where you don't need a control surface, yet you are free to make your own scenes and chases as you see fit(or unfit, I won't judge).