From Schiphol airport it is a 40 minute taxi ride to Utrecht. Taxi's can be found at the official taxi point outside of the airport. More conveniently you can find a direct connection from the Schiphol airport train station to Utrecht Central station which is a 30 minute train ride. Tickets can be bought at the yellow machines in the station, at the service desk but also booked in advance on-line here.
A taxi ride from Eindhoven can be a bit expensive. Most conveniently is to take the shuttle bus to Eindhoven central station from which you can take a direct train to Utrecht Central station. A combination ticket for both the shuttle bus and train ticket to Utrecht central station can be bought in advance here.
When staying in Holland, do as the dutch. As you will see on your arrival, the people in Utrecht mainly use their bicycle as their mode of transportation. You can rent a bicycle from the dutch railroads, the so called OV-fiets. These are available at the bicycle parking on both sides of Utrecht Central Station. For more information on reservations and prices, click here.
Most areas in Utrecht are easily accessible by public bus. Tickets can be bought in the bus (for an extra fee) or you can buy an anonymous ov-chipcard at the train station (both valid for train and bus). For more information how to get and use an ov-chipcard, click here.