Best way to get in town is using the railway line, that will rapidly connect you either from La Spezia side or Levanto side. Trains are the best way to move around the Cinque Terre coastline, trains run every 20min back and forward the National Park, from April to October. Genova-Santa Margherita-Chiavari (west side of Liguria) is very well connected to Cinque Terre Area; same for Tuscany side, Pisa-Firenze-Lucca, connection to La Spezia and then change to Cinque Terre.
For more information about train schedule visit the website https://www.trenitalia.com or download the Trenitalia App
If you really want to reach Cinque Terre by car you have to consider that in Monterosso, being a very small town, we frequently have parking issues, both parking area get fully booked very easily (there's no way to secure a spot ahead) Monterosso is a traffic free area, except for special requests (such as people with disabilities), you'll have to park your car at the border of the village and walk to the dock. Main parking areas in town are "parking Loreto" or "parking Fegina", both of them 10 and 15min walking to the dock.
Nearest highway exit are A-15 La Spezia (1,5 hours driving to Monterosso) or A-12 Levanto/Carrodano (45min driving to Monterosso) both roads that connect from highway to Monterosso are curvy roads.
*we will consider eventual delay due to parking issue as a no-show, charging the full amount.