There are several busses daily from Dar which you can get from Ubungo, Temeke or Mbagala bus stations. 8+ hours note that during the rainy season parts of the road can get flooded. It's usually still passable but this can add significantly to the journey time. The companies operating the route change regularly but when picking a bus go for one with four seats in a row, the ones with five can be pretty cramped. Sitting in the back half of the bus can be somewhat traumatic during the non-paved part of the journey.
From Lindi there are buses throughout the morning, in the afternoon you can make the journey by first getting a bus to Mnazi Mmoja Mingoyo then catching an onward bus from there. ~2 hours
From Mtwara there are daladalas minibuses throughout the day from around 6am to around 7pm about 30 minutes. Alternatively, you could get a taxi around 10'000/-, a tuktuk bajaji around 6'000/- or a motorbike pikipiki around 4'000/-.
From Masasi there are buses throughout the day the last one leave around mid afternoonabout 4 or 5 hours
From Newala and Mozambique you'll have to go via Mtwara.
Precision Air also fly from Dar to Mtwara, the timetable is highly erratic.
