From Utrecht Central Station it is a 15 minute walk to the Domsquare. I recommend walking as it often is just as fast as taking a bus.
Bus number 2 stops at the Domsquare. Also busstop Janskerkhof is close by and is attended to by many lines. Check the website 9292.nl for travel schedules and timetables.
Car Park
Parking on the streets is possible but expensive and oftentimes it is hard to find a spot. Below you will find car parks close to the Domsquare. Sometimes reserving a spot beforehand is cheaper. You can also check out Parkbee for this.
Parkeergarage Springweg - A 5 minute walk to the Domsquare. Costs: 2 euro per 25 minutes / 36,- per day
Parkeergarage Hoog-Catharijne P1 - A 10 minute walk to the Domsquare. Costs: 0,50 cent per 9 minuten / 30,- per day
Park and Ride
The cheapest option is using the Park and Ride locations Westraven and Science Park. Parking costs 6 euro´s per day and includes a bus/tram-ticket for up to 5 persons. I couldn´t find propper updated English instructions on how to use the P+R´s. I suggest following the links below and use Google translate instead.
P+R Westraven is located south of Utrecht next to the A12 highway. Here you can take a tram that will take you to Utrecht Central Station in 12 minutes.
P+R Science Park is located east of Utrecht next to the A28 highway. Here you can take bus 28 (or tram) that will take you to the city centre in 15 minutes. I recommend getting of at Janskerkhof close to the Domsquare.