Public transportation brings you to the border. To/from Sudan or Kenya you just walk to the other side. If you arrive at the border towns late at night, try not to cross the border in the dark. Wait in the town and do your traveling in the morning.
Buses that cover some distance start in early morning. This implies that if you arrive during the day you would be stuck at least until the next morning.
From Gedaref Sudan catch a bumpy bus or truck 700 SDnr to the border. The Sudanese side consists of several small villages and a tiny town. In Ethiopia you could find better, but basic, accommodation. Buses leaving for Gonder dry up by mid-afternoon so you must either arrive early at the border or spend the night in Metema around 50 birr.
From Djibouti you can take a small bus to the border 2-3 hr where you will find buses to Dire Dawa. This road is a dirt track and the trip takes at least half a day, at nightfall the bus uses to stop and you resume travel the next day. From Ethiopia into Djibouti, a bus leaves supposedly around midnight buy tickets during the day at the office in the centre of Dire Dawa. This arrives at the Djibouti border in the morning where you change onto a different bus to get to Djibouti City. It is a good idea to take a tuk-tuk to the bus station as hyenas wander the streets of Dire Dawa at night.
Ethiopian Airlines is one of the most successful and reputable airlines in Africa. Bole International Airport in Addis Ababa is the main hub for Ethiopian Airlines and also hosts Lufthansa, Sudan Airways, Kenya Airways, British Airways, KLM, Turkish Airways, Emirates, Gulf Air, Egypt Air and fly Dubai. A new runway and international terminal, which was said to be the largest in Africa, opened in 2003.
CAUTION: Arriving in the country without a major currency such as euros or US dollars is not recommended, especially if one has not obtained a visa prior to arrival. Travellers cheques and cash can be exchanged at the airport.
If you have a prior arrangement, many hotels will send a vehicle to pick up pre-booked guests from the airport.
Other international airports are in Dire Dawa, Mekele and Bahir Dar.
Ethiopia is landlocked and currently uses the seaport in Djibouti. From there, Ethiopia can be reached by bus or car following a good road to the border and a dirt track from there onwards.There is a navigable river called Baro in Western Ethiopia that connects Gambella town to the Sudanese Capital Khartoum. But river port at Gambella has been closed for decades.
One way to get in from Sudan is via the border village of Metema.
One way to get in from Kenya is via the border town of Moyale. The road from Kenya to Ethiopia through the town of Moyale is much better and well maintained. On the Kenyan side of Moyale the road is horrible and is known for banditry so be careful and make sure you have plenty of time, at least 24 hours, to travel from Moyale to Nairobi.