Taking train from San Jose to San Luis Obispo?

This is my first trip by train in USA, and I'm a international student. This is my third week here in USA. So I'm really confused about taking train to San Luis Obispo. I need to visit my host family in Grover Beach, and my current city is Cupertino. I think San Jose is the nearest train station. Which train should I take to arrive in San Luis Obispo? Could you please give me the link of the website that I can book the ticket? I'll travel alone, so I don't wanna get lost. Please please anyone help me. Is it right to take train from San Jose Caltrain Station?? Thanks for your help.