In all likelihood, you will arrive at a remote stand (only a handful of jetways in Addis) so you will be bussed to the terminal. Go up the escalator (faster to use the stairs if you are trying to beat the crowds) and then head straight in the direction that the stairs bring you up towards the center of the terminal. If you arrive on a jetway, then follow the signs for Transfers and Arrivals (they head in the same direction initially).

When you come to the escalators going down to immigration and baggage claim, the transfer desk is on the left. You can't miss it. They will give you a voucher (you may or may not get the plastic token - last two times they didn't give me one and immigration just stamped the back of my onward boarding pass rather than the passport) that has hotel details on it, plus a list of the meals to be provided at the hotel.

Take the voucher and go down the escalators towards immigration. Go through immigration (NOTE : DO NOT stand in the visa-on-arrival lines if you have the voucher and/or token - go straight to the counter). You will be fingerprinted and photographed. Just before exiting baggage claim (after the Customs X-ray machines but before entering the public area) there is a waiting area on the right for hotel shuttles. If you want to get some Birr, there are ATMs in the customs area right next to this. Take a seat and listen carefully for the relevant driver yelling your hotel name at the appropriate time. There is usually an ET staff member on hand there to assist as well.

The system is a well oiled machine since ET puts hundreds of pax through it every single day. The hotel will arrange your meals, wake up call, shuttle back to airport and everything else you need on ET's account.

PS. Since you have a schedule change, it is likely that ET will have your voucher already printed at your first check-in point. In this case, you will still need to stand in line at transfers to get your specific hotel assignment. Don't make the mistake of going down to immigration without the hotel assignment - they will just send you right back upstairs and then you'll be stuck at the back of the line!