Start off learning common Egyptian phrases in writing. The blog Egyptian Arabic Dialect Course is a great place to start. This blog offers 15 free lessons of Egyptian dialect. However, you can search any number of similar websites and blogs online.
Search iTunes and the Internet for language learning podcasts. Egyptian Arabic Podcast is a good example of a podcast that is available online and on iTunes.
Search YouTube for Egyptian dialect tutorials. Complete the audio exercises at home or in an environment where you will feel comfortable practicing out loud.
Listen to Egyptian songs and TV shows. Many are available on the Internet and YouTube. Dialect is best understood in context, as in conversation or song. Also, such immersion is the best way to retain a language.