The fort is about 6km from Kilronan, the main town in Inis Mor where the ferry comes in.  Many people bike to Dun Aengus, either with a regular bike or an electric bike (eBike).  As a bike hater, I strongly recommend the latter.  It will take from 25 to 60 minutes depending on your speed and how often you stop for photos.
Other options include taking a tour of the island with a taxi van (what I did, given limited time and bad weather) or a pony trap tour of the island.  If you have plenty of time and energy, you could walk there as well.  It's not exactly a flat road, so expect some smaller hills up and down.  The ‘low road’ is the best route to cycle to avoid the worst hills.