travel from Zurich to Lucerne

The train is very convenient. "Best" might depend on if you have special needs of any sort.

It is about a one hour, easy train ride. Trains are very efficient in Switzerland and the staff at the ticket counters tend to speak English and are very helpful.

Beb, do you mean Zürich airport or Zürich city centre?
Either way, it will take ~70 minutes by train, and there are multiple departures per hour. Look up times on the SBB (Swiss Federal Railways) website: https://www.sbb.ch/en

• The station at Zürich airport is called "Zürich Flughafen"
• The one in the centre of Zürich is "Zürich HB"
• The one in Luzern (local spelling) is just called Luzern
• Zürich Flughafen to Luzern cost CHF 30.00. That ticket is valid on any train that day, you just buy a ticket at the station, which is an undercover walk from the terminal.