The Center for Instructional Innovation participates in University assessment efforts on many levels. For us, assessment is about reflection in action and measuring performance in the service of continual improvement. Assessment is about getting better, not getting by.
One of the easiest ways to accustom yourself to assessment procedures is to reflect periodically on the success of a given class or unit within a class. You do this naturally, of course, by thinking about how it went, but you can do it more systematically by asking your students for quick-take feedback. There is an added benefit here in that you will be able to see if the students "got it" or not. For this you might consider using a "fast feedback form (pdf)" or a "minute paper (pdf)." You might also consider a "critical incident report (pdf)." If you are technologically inclined, you might consider using clickers in your classroom to regularly test the intellectual temper of the room. If you do these forms of periodic formative assessment practices online, using a list serve or even just an email system, you can retain data of student learning over time and this will give you a leg up when it comes time for your annual teaching report. Such data might also prove useful one day for research purposes.