The nearest airport to Utrecht is Schiphol Amsterdam. From Schiphol there is a direct connection to Utrecht, trains leave every 15 minutes. It takes approximately 30 minutes to get to Utrecht Central station.
Many of the low cost airlines fly into Eindhoven Airport. From Eindhoven airport you can take a bus to the train station. From Eindhoven Central station direct trains to Utrecht leave every 15 minutes. It takes approximately 50 minutes to get to Utrecht Central station.
You can buy a ticket at the ticket machines at every train station in the Netherlands.
There are also other Dutch, German or Belgian airports available after which you can take a train to Utrecht.