Given that we were staying in Oia, we started from the Oia side and made our way to Fira. I personally feel the trek would be better the other way around. Starting in Fira and finishing in Oia allows for you to start in a busier area where you can grab coffee and breakfast and then finish in more natural, quieter surroundings.
The walk takes you through Oia, Finikia, Imerovigli and Fira and has a constant view of the coastline and sea. Part of the enjoyment is that it’s not heavily signposted. Although, at one point we followed a trail around a caldera that turned to a steep drop down at the end. Be wary of this and exercise caution. It may mean you have to follow a road for a while.
When you finish in Fira, there are a lot of options for brunch or lunch and plenty to see in the area too. Being the islands primary commercial hub too, you will easily be able to catch a bus to wherever you are staying on the island.
We were exhausted after the walk and only spent an hour so exploring Fira before heading back to Oia.