Flights leave Dar es Salaam on an almost daily basis to Mtwara.
You can also catch a weekly ferry from the port at Dar es Salaam to Mtwara, be warned it can be cramped and uncomfortable.
There are daily buses leaving Dar es Salaam that run down the coast through Kilwa and Lindi before arriving at Mtwara.
Basic Buses run between all the major towns in the area and smaller dala dalas run between the surrounding villages.