Amsterdam to Groningen train?

Use the official rail site of the Netherlands
https://www.nsinternational.nl/en

There is only one train line, which is run by NS, the Dutch national railways. Use the train planner mentioned by Jazz+Travels and you'll see an excellent half-hourly connection with only one change, at Utrecht Centraal. (The train planner will also show an ICE train for the leg Amsterdam-Utrecht. Don't pay it attention.)
Advance buying of your ticket is not necessary (domestic trains in the Netherlands don't come with seat reservation). Online buying is 1 or 2 euro cheaper than getting them from a ticket machine or at a window at the station.

Thanks to both you both. I thought I read somewhere that the self serve ticket machines at the train station do not take foreign credit cards. Do you know if that's true? Thank you, Jennifer

They are supposed to work with Visa, Maestro and American Express. If your card doesn't work, you can always use the ticket window.

Thanks so much.