Some authors make it easy for their fans to read their series in order. Sue Grafton gives us her books in alphabetical order and Janet Evanovich gives us numerical order.
How do you find out about other series, though? It is always good to start with the first book in the series to avoid "spoilers" in subsequent titles. In the Brother Cadfael series, for instance, someone who is the Benedictine's best friend in later books is a major suspect in book one. That kind of ruined the first book for me when I finally got my hands on a copy after having already read book seven.
You can't always go by the publication dates in the Library catalog. If you did a "sort by year" on Martha Grimes, the oldest title listed would be The Old Fox Deceiv'd. The first book in the Richard Jury series is actually The Man with a Load of Mischief, but this has a later publication date than many of the other titles because we had to get a paperback replacement for the original.
What to do? I suggest you bookmark the fantastic fiction website.
Try finding Robert B. Parker by clicking on "P" in the "browse authors" box in the upper left hand corner and then select "Paul Park-Allison Pearson" from the "jump to" list. Find Parker's name and click. A list of his books will come up for you, all neatly broken out by his detectives Spenser, Stone and Randall in the order in which they were published.
Have fun!
If you know of any other good sites, please share them with us.