Pay at the counter
Every train station except rural stops has a ticket counter, where you can buy tickets for immediate departure or up to 90 days in advance. They take cash and ask no questions (other than your destination and departure date). Larger stations have a dedicated Reisezentrum (travel center), in smaller stations the counter may be hidden in the snacks/newspaper/convenience shop, or there is a travel agency in the station building.
Called Fahrkartenautomat. They were recently overhauled, all of them should take at least €50 notes, I'm not sure about €100. They can speak Spanish.
On the train
You can buy a ticket for cash onboard on long distance trains, but then there is a surcharge of €7.50 (AFAIK). Warning, this is only possible on long distance (IC, ICE) trains, not on local ones like RE,RB or S-Bahn.
Even if you don't have a card, you might be able to open a Paypal account, transfer some funds in advance, and book tickets online. You should definitely check out this if you know the exact time when you would travel, since there are substantial discounts available when booking a few weeks in advance, e.g. €49 instead of €114 just for the Frankurt - Zürich leg. You'll need you passport number for tickets booked online. Note that discounted tickets are not refundable on or after the day of departure.