The nearest airport is Dalaman, 25km west, served by direct flights from across Europe in summer. Taxis to Dalyan take about 25 minutes; shared shuttles (often arranged by hotels) are cheaper. There are also local minibuses (dolmuş) via the town of Ortaca — slower but very cheap.
If you're already on the Turkish coast, Marmaris is the nearest large town (about 2 hours by road) and there are dolmuş connections via Ortaca and Köyceğiz.