The Excel files in the links below contain actual ridership counts in a format we call "entry-exit" matrices. Each page shows the average ridership for the month by type of day (weekday, Saturday, or Sunday) in a matrix, 44 stations by 44 stations. We also have trips taken on BART using Muni's Fast Pass fare instrument.
So, here's how to read the data: If you look across the top of the page, each station listed in Row 2 is the station of entry. Look down Column A to find the station of exit. So, for example, on the typical weekday in July 2010, 399 people entered at Richmond Station and traveled to Berkeley Station. And, heading in the opposite direction, 374 people entered at Berkeley Station and traveled to Richmond Station. Easy!
The files are automatically updated and are usually available by the 5th of the next month. You may need to reference this list of station name abbreviations (.pdf).