Many reviews and online resources discuss taking the Ravenna city bus to visit this popular monument, located several kilometers from Ravenna proper.  However, they can be light on details, making for a somewhat more stressful experience than necessary.  Here are some specific instructions for reaching the church.

The number 4 bus leaves from the Stazione (railway station).  It can also be picked up elsewhere in town, but this is the most accessible location for most visitors. (Ask your hotel/host if they have an alternate suggestion, but beware--they may have never taken it themselves.)  You can purchase two tickets ("andata e ritorno") at the magazine stand just  inside the stazione.  The stop ("fermata") for the #4 bus to Classe is across the street from the Stazione, to the left as you face away from the entrance.   It's stop #5, and there's a bus shelter as well as timetables posted for several buses, including the 4.  (This is how you'll know you're at the correct stop--the timetables for #4.)  This bus also stops on the Stazione side of the street on the return.  You cannot pick it up there if you are outward bound.  

The #4 runs every 20-30 minutes, so you may have to wait a while.  When the bus arrives, climb on (you can ask the driver "Va a Classe?" if you're unsure) and insert your ticket in the orange reader at the very front.  It will pull it in, then push it back out for you.  The ride to Classe takes about 15-20 minutes.  The bus winds through Ravenna, then out into the countryside, then takes a long loop through the village of Classe before returning to the main road to resume its route.  Soon after this loop, you will see the church with its bell tower on the left.  Right before you get to it, push the blue button beside you on the wall of the bus, between the windows.  That will signal you want a stop.  The driver will stop at a bus shelter about 350 meters past the church.  You can cross the street and proceed back the way you came to the church, passing a hotel and restaurant along the way (5 minutes or less walking).  Entry fee as of May 2015 was 5 euros.  You can also buy a combined ticket with two other, much lesser-known monuments. 

This church and its mosaic decoration was begun in the Early Christian era and completed after the Byzantine emperor Justinian's annexation of Ravenna into his territory in the mid 6th century CE.  Many guide books are available in the bookstore and resources are also found online that explain in excruciating detail the intricate iconography and history of the apse mosaics.  They are considered a major monument of world art, taught in most college art history surveys, and you're unlikely to be disappointed seeing them in person.  

After your visit,  you'll need to find the return bus stop.  As you exit the church, look towards the main road and to the right.  You'll see another bus shelter, this time on the church's side of the road.  Use your second ticket that you purchased earlier for this return trip, which does not make the loop through Classe for some strange reason.  Depending on how long you have to wait for buses, and how much time you spend in the church, the entire trip can take under an hour.