Inis Oirr is reachable by sea from both Galway and Doolin, or by air from Connemara.
From Galway: Aran Island Ferries runs two boats daily from Rossaveal (Ros an Mhil) in Connemara, with a connecting bus from Galway city. The crossing takes about 45 minutes.
From Doolin, Co. Clare: Three ferry companies operate from Doolin pier to Inis Oirr from roughly April to October. The crossing is short — about 20 minutes in good weather — but can be rough when the Atlantic is up.
By air: Aer Arann Islands flies daily from Connemara Airport (near Inverin) to all three Aran Islands. The flight takes about 10 minutes and the views are spectacular.