There are two major ways to actually estimate inter-rater reliability. If you measurement consists of categories -- the raters are checking off whichcategory each observation falls in -- you can calculate the percent of agreement between the raters. For instance, let's say you had 100 observations that were being rated by two raters. For each observation, the rater could check one of three categories. Imagine that on 86 of the 100 observations the raters checked the same category. In this case, the percent of agreement would be 86%. OK, it's a crude measure, but it does give an idea of how much agreement exists, and it works no matter how many categories are used for each observation.

The other major way to estimate inter-rater reliability is appropriate when the measure is a continuous one. There, all you need to do is calculate the correlation between the ratings of the two observers. For instance, they might be rating the overall level of activity in a classroom on a 1-to-7 scale. You could have them give their rating at regular time intervals (e.g., every 30 seconds). The correlation between these ratings would give you an estimate of the reliability or consistency between the raters.
You might think of this type of reliability as "calibrating" the observers. There are other things you could do to encourage reliability between observers, even if you don't estimate it. For instance, I used to work in a psychiatric unit where every morning a nurse had to do a ten-item rating of each patient on the unit. Of course, we couldn't count on the same nurse being present every day, so we had to find a way to assure that any of the nurses would give comparable ratings. The way we did it was to hold weekly "calibration" meetings where we would have all of the nurses ratings for several patients and discuss why they chose the specific values they did. If there were disagreements, the nurses would discuss them and attempt to come up with rules for deciding when they would give a "3" or a "4" for a rating on a specific item. Although this was not an estimate of reliability, it probably went a long way toward improving the reliability between raters.