Ethiopia is a curious mix of social conservatism (many Ethiopians are deeply religious) and a fairly relaxed approach to life. As a general rule, you're more likely to find the latter in Addis, and the former in rural areas and smaller towns. To be on the safe side, modest behaviour and dress in public areas is almost always the way to go. While you may be forgiven as a foreigner for stepping over the line, you should still try not to offend and always seek local advice if you're unsure.
Ethiopians will almost always seek to behave respectfully to one’s elders and we encourage you to do likewise. Greetings are important to Ethiopians so take the time to greet people properly before launching into the main business of the conversation.
Eating is one area where it pays to try and replicate local customs.