Most frequent flier programs place Ethiopia into the Africa zone. You can find some generic recommendations on how to get to East Africa here. I already have a blog with my recommendations for which programs to join if you are new to the world of miles and points.
The major gateway city for Ethiopia is Addis Ababa. Once you have been in the miles and points game for awhile, you will get a feel for which airline to use where but if you are just starting out Wikipedia will show you all the airlines that fly into Addis Ababa.
The only One World member serving Addis Ababa is Qatar Airways via Doha. You can reach Doha from anywhere in the world where Qatar flies to.
Ethiopia’s national carrier, Ethiopian Airlines is a member of Star Alliance so you can get just about anywhere in Africa via Addis Ababa. If you are only connecting, even on a miles award ticket and you have an overnight connection, Ethiopian Airlines will give you a free Visa and accommodation with meals.
Other Star Alliance carriers serving Addis Ababa include Egypt Air via Cairo, Lufthansa via Frankfurt and Turkish Airlines via Istanbul.
From Europe you can use Egypt Air via Cairo, Ethiopian Airlines, Lufthansa via Frankfurt or Turkish Airlines via Istanbul.
From Australia and New Zealand there are no direct flights, you need to get to Singapore or Bangkok, then you can pick up Egypt Air, Ethiopian Airlines or Turkish Airlines.
From North America you can use Kenya Airways via Europe.
From Europe once again Kenya Airways via Nairobi is the only option.
From Australia Skyteam isn’t the best option unless you travel via Dubai and pick up Kenya Airways from there.
Emirates serves Addis Ababa from their hub in Dubai with connections world wide.
HOW MANY MILES WILL IT COST?
Every airline member of the 3 main alliances has it’s own frequent flier program. Examples are in my East Africa post.