With the growing stature of Ethiopian Airlines and ADD as a major African aviation hub, I believed its time to have a complete guide to the airport. Since the airport does not have a functioning website, and the Ethiopian Airlines website does not give clear information, I will try to make this guide as comprehensive as possible. Feel free to add on, and reply with questions !
TERMINAL 1
This terminal is used by DOMESTIC and Regional Flights.
Airlines:
Ethiopian Airlines (Domestic as well as JIB, HGA, JUB, JED, RUH, KWI, DOH, BAH, MCT, DAM)
FlyDubai
Qatar Airways
GulfAir

This terminal is rather outdated and lacks in practically any amenities.
Lounges:
Ethiopian Airlines Lounge (For Cloud Nine, ShebaMiles Platinum/Gold, and Star Alliance Gold)

There is one security checkpoint near the gates, and all gates (15-18) are connected after security

TERMINAL 2
This is the primary International terminal and unless you are connecting to one of the cities listed in section above you will remain in this terminal.
Airlines:
Ethiopian Airlines (all other destinations)
Emirates
Lufthansa
Turkish Airlines
EgyptAir
Saudia
Kenya Airways

Guide to Connections:
You have a 90% chance of arriving at a remote stand and will be bussed to Terminal 2, no worries this still a relatively simple process. After arriving at the terminal, all passengers will ride a quick escalator ride up to the arrivals mezzanine. If you luckily arrive via jetbridge, you will arrive directly into the arrivals mezzanine. Once on this floor follow the CONNECTING FLIGHTS sign (The sign is in Green). In the center of the terminal is where you will either follow the CONNECTING FLIGHTS signs and proceed on the escalator to the Departures level or proceed downwards to IMMIGRATION AND BAGGAGE CLAIM. Just follow the GREEN signs and you will find your way, plus there are always lots of agents screaming "TRANSIT TRANSIT" to point you in the right way lol.

If you have a long transit in Addis Ababa and will be accommodated by ET then at central point next to the escalators that take you to departures, proceed to the "ARRIVALS AND TRANSFER DESK" where ET ground staff will gladly assist you and provide you with your voucher.

Departures:
This terminal is standard and has free WiFi but doesn't have many eateries, the bathroom are not in the greatest condition, and shops are overpriced. Overall a decent experience, but can get very crowded during the morning from 6-10:30 AM and evenings from 7:30pm-2AM.

Lounges: There are FOUR and each of them have strict entry rules
1) Cloud Nine Lounge: this is for Ethiopian Airline Cloud Nine Passengers as well as Business Class passengers of other Star Alliance flights.
Location: in the back row in the center of terminal
2) Star Gold Lounge: this is for Star Alliance Gold Members only
Location: in the back row towards the left
3) Platinum Lounge: this for Sheba Miles Platinum Members only
Location: in the front row, center, near the Gold Track checkpoint
4) Ethiopian Lounge: this is for ShebaMiles Silver Members
Location: in the back row on the far left side

*Important to note: Security at ADD is done at the gates
Just look around at the screens and when it says "Proceed to Gate", I would strongly advise you to proceed as security lanes can get very long.
Guide: There are 4 main security checkpoints, and an additional 1 for Star Gold Track (Cloud Nine, Sheba Miles Platinum/Gold, Star Alliance Gold)
Gates 1-7 are bus boarding gates with standard security
Gates 8-9 are jet bridges with standard security
In the Center of the Terminal is STAR GOLD TRACK with standard security
Gate 10 jet bridge with standard security
Gates 11-14 house high security flights to USA, Canada, Israel, UK and occasioanlly flights to other destinations. This checkpoint can take up to an hour at peak time. (Gates 11,14 are jetbridges 12 &13 are bus boarding)

*Security is rather tight at ADD, shoes and laptops have to be removed. Gates 11-14 additionally require disposal of water bottles and utilize TSA like body scanners
*Gates 1-10 are connected after security, Gates 11-14 are walled off from the rest
** IF YOU ARE ALLOWED TO USE THE STAR GOLD TRACK USE THIS LANE, IT IS MUCH QUICKER. However, if you are departing from Gates 11-14 you must use that checkpoint, there is a Priority line however.
** For those passengers who can utilize the STAR GOLD TRACK, there is a pleasant waiting area near Gate 10 after the checkpoint where when boarding for your flight begins you will be taking down an exclusive elevator down to busses, or will go to your jet bridge if your flights departs from one.

Arrivals:
For passengers who are terminating in Addis Ababa and for those who have received their voucher, follow the IMMIGRATION AND BAGGAGE CLAIM signs, at the central part of the terminal, proceed on the escalators down to Immigration. Once in the Immigration hall, the right 2/3 of counters are for Ethiopian citizens/Origin ID cardholders/Permanent Residents and Foreigners who already have a visa. If you completed an e-visa or are completing a Visa on Arrival stay on the left 1/3. There are signs to point towards this.

Baggage Claim hall is to the right of immigration counters, just look at the screens, and remember all Priority (Cloud Nine, ShebaMiles Platinum/Gold, Star Alliance Gold) bags will are at Carousel#2 regardless of origin. Before proceeding to customs there will be a security check to verify your checked bags match the number on bag tags given to you at check-in. (If you are on an overnight ET voucher skip this point and walk past customs where there this a little waiting area where you can wait for your respective hotel and/or ET pickup bus). Now once you leave the arrivals hall, you enter what used to be the meters/greeters area (meters/greeters now have to wait in the parking lot due to construction in the terminal) but now simply house booths for the hotels. If you have someone waiting to pick you up, you will proceed outside and walk down a ramp into the parking lot where you will find your waiting party.

Hope this makes sense !