Schedule enough time in the end user work environment so you can (a) get a good look at the entire task or work process that will be impacted by the project result and (b) avoid the impression of a disinterested manager doing a half-baked 'fly-by'. (Priority is measured in minutes, so when you invest fewer minutes in an end-user's environment than they think is required to really understand what they do, you run the serious risk of disrespecting them.)
Don't just 'show up' and stare at end-users as they do their work. Make an appointment, arrive on time, introduce yourself to people (smile) and explain that you're there to learn enough to help them with (state the project purpose). Ask for their permission to just observe for a while and let them know that you'll ask questions later, when questions won't disrupt their (important) work.
In addition to looking for ways that your project will accomplish the intended result, look for (a) additional benefits that could be realized with slight changes in the project scope, (b) ways to measure baseline and post-project productivity (for ROI estimates and post project actuals) and (c) the starting point that your training will begin at in order to bring end-users up to speed with your project result.
When you talk with end-users, make a point of showing them your notes as you ask questions, (eg. "I noticed that you (point toward notation) did 'X' when 'Y' happened and I was wondering if that step might be more convenient if we did 'Z'? What do you think?"). By demonstrating that you have nothing to hide and that you're interested in their ideas, you'll generate much better fact finding results.