If you land at Lugano Airport you can reach Locarno by taxi (from CHF 150.--) or by train via Lugano.
Trip by train:
You can reach Lugano railway station by taxi (CHF 30.--) or with a shuttle service or by train from the station in Agno (10 minutes walk from the airport).
From Lugano there are connections to Locarno every 30 minutes, with one change in Giubiasco.
The total trip by train from Lugano-Agno to Locarno takes about 2 hours.
Advance booking of train tickets within Switzerland is possible but not obligatory.
On the SBB webpage you can find the most convenient train schedule for you.
Once in Locarno, continue to Monte Verità by following the directions given.