I'm staying at the Hilton at Logan next week, and need to get to Natick on Saturday afternoon. I believe there is a commuter train that goes that way. What train will I need to take and where can I get info on times?

Better yet is Logan Express which goes to Framingham/Natick
http://www.massport.com/logan/getti_typeo_logan.html

You would have to get to South Station, and then take the Comuter Rail.....here is the Saturday schedule:

http://tinyurl.com/hxvg9

mbta.com lists bus, train, commuter rail schedules, which will all be less frequent on Sat afternoon than rush hour.

If you're staying at Logan anyway, absolutely take the Logan Express to Natick. Couldn't be more convenient and fast. Just get a shuttle bus from the hotel to one of the terminals and look for the signs. You pay on board. Much easier than getting to South Station. (I used it last week to get to/from Braintree and highly recommend it)