Dire Dawa Airport (DIR) is 3 kilometres west of the centre, with several Ethiopian Airlines flights a day to and from Addis Ababa (about an hour). It is by far the easiest way in.
The new Addis Ababa–Djibouti Railway runs through Dire Dawa with Chinese-built electric passenger trains a few times a week — about 8 hours to Addis or 2 hours to Djibouti. The new station is north of the centre; check current schedules locally.
By road, Addis Ababa is about 450 kilometres west on a tarred but slow highway (10–12 hours by bus). Harar is 50 kilometres south, an hour by shared minibus from the Megala bus stand. The road to Djibouti is open but the border can be tedious.