Train from Dijon to Lucerne

by taking the train.
try sbb or sncf sites for schedules fares that day

Could you please let me know where to get info--price, schedule, etc. for that train.

Patty, as Jazz said, you go to the website of the company operating the trains. In this case that would be:
either SNCF (French Railways): http://www.sncf.com/en/passengers
or SBB (Swiss Federal Railways): https://www.sbb.ch/en/

I went to the SBB site, typed From: Dijon Ville, to: Luzern, date Tue 12.09.2017, time: 09:00 and got a whole list of trains throughout the day. The fastest took 2h54 with 2 changes:

Dijon Ville dep 12:01, Basel SBB arr 13:26
Basel SBB dep 13:31, Olten arr 13:55
Olten dep 14:06, Luzern arr 14:55

Prices started at CHF 85.
A good site for buying tickets if you are in a foreign country is: https://www.trainline.eu/

For lots of info about travelling by train, I recomend this site: https://www.seat61.com/

Thank you so much.