Geneva to Zurich

You can get schedules and fares at the Swiss Rail site: rail.ch

There are direct trains every 30 minutes, simply purchase your tickets at the station on the day of your journey. No need to make any sort of advance reservations.

Your other posts said that you have a Eurail pass. If you pass covers Switzerland, then you can just jump on this train using a rail pass travel day. Otherwise, fare is $90 per person in 2nd class.

Laura, The standard fare Geneva to Zürich HB, second class single is CHF 87 (87 Swiss Franks), not $90!
The currency of Switzerland is Swiss Franks, not "$" (of which there are many types). [end rant]

Falalaah, There is no need to make reservations on Swiss trains, it is not even possible to make bookings on Swiss internal trains except for a few tourist routes. Swiss rail fares are fixed, all tickets are valid on any train, and there is no discount for advance booking.

"...it is not even possible to make bookings on Swiss internal trains
except for a few tourist routes..."

Not so. From the Swiss Rail site:
"You can reserve your seats on Swiss trains in the SBB Ticket Shop, using SBB Mobile on a smartphone and via Rail Service 0900 300 300 (CHF 1.19/min. from the Swiss fixed-line network) or direct at the ticket counter. It costs CHF 5 per seat to make a reservation."

That must be something new with Swiss trains. It always used to be (for me up until last August) that everybody piled on all the trains and found whatever was free.

The only exceptions used to be trains (EC or TGV or ICE or RJ) which crossed international borders and the first class sections of some named tourist trains.

I can't remember the internal trains, double decker or single decker, even having places for paper reservations to be put, or electronic reservation boards. I wonder how they indicate that a seat is reserved?

The reservation scheme has been in place since at least the 90s. On IC trains there are place holders above the seats for paper strips indicating reservations, similar to the older DB carriages. You probably didn't notice them because it's rare for anyone to actually make these reservations.

I agree with Nigel, from many years of travelling on Swiss trains I have never seen a reserved seat, except on trains that cross the border. But I did find this reference (only in German)

Einzelsitzplätze sind in den meisten Intercity (IC)- und ICN-Zügen reservierbar. Entsprechend der gewählten Verbindung sind jeweils auch zonenspezifische Sitzplätze (z.B. Business-Zone oder Familienabteil) online buchbar.
Eine Reservierung ist fest an eine konkrete Verbindung gebunden und kann nach der Buchung nicht mehr angepasst werden. Kein Umtausch, keine Erstattung.
Dieses Billett erhalten Sie als OnlineTicket. Bitte beachten Sie die speziellen Bedingungen für OnlineTickets.

So it looks like you can book, but only if you buy an online ticket which is only valid on a specific train.
Normal tickets are fixed price, and valid on any train. There is no option to select a train when buying a ticket at a ticket machine, and that is how most tickets are sold.

Per the Swiss Rail site reservations can also be made at the ticket counter at the stations.