Online resources for learning the Ethiopian alphabet include Omniglot.com, which offers several free resources for learning the language known as Amharic. The site includes a list of the syllables, their pronunciations and English equivalents. It also includes punctuation, numbers, a sample paragraph and links to other free resources.
Omniglot.com's page does not have all of the information you need to learn the language, but memorizing each of the characters and their pronunciations is a good way to start. After learning the characters, choose another resource that suits your reason for learning the language. For instance, if you intend to visit Ethiopia for a short time, use a resource such as Internetpolyglot.com. This site offers several different games designed to teach Amharic that are focused around the most common words needed from day to day.
On the other hand, if your plan is to move to Ethiopia or spend a long time there, consider purchasing a more comprehensive lesson. InstantImmersion.com offers a program in Amharic for beginner and intermediate speakers. These programs often focus on speaking more than reading but do cover both to some extent. They are usually comprehensive enough to give you an idea of the cultural contexts in which different words and phrases are used.