Is it possible to get from Tel Aviv to the Caesarea ruins by train?

There is a train stop called "Caesarea - Pardes-Hana " I assume you'd have to take a bus or taxi from there to the ruins. Here's the website for the rail system
http://www.israrail.org.il/english/index.html

Take the train from each of Tel-Aviv's stations going north towards Haifa and stop at either Pardes Hanna or Benyamina (About 35 minutes). Then take a taxi to Caesarea ruins (About 10 minutes) (There are no direct bus lines). It's worth the effort. Dont miss the multimedia show. www.caesarea.org.il [email protected]
See the ruins and the harbor and walk out of the old city south along the beach to the Hypodrome.

Thank you for the information. Do you happen to know if there is a taxi stand at the Pardes Hanna or Benyamina stations?

At many busy stations in Israel , taxis come by regularly. If not, you can always ask someone (at the restaurant or newstand at the staion ) to call for a cab--I'm sure they'll have a phone number handy

These are quite small places. Nevertheless taxis are usually not difficult to find. Here are some local taxi station's phone numbers:
'hanadiv' (04)-6271171 052-2419350 050-5391678'
'hamoshava'(04)6371811
'hashelosha' 052-4300605
You use the 04 when calling from another zone and when using a cellphone.