EgyptAir is the main domestic carrier. Nile Air also flies between Cairo and the main centres, though it has fewer services. Fares for both airlines can be surprisingly cheap. Domestic one-way fares on EgyptAir start from LE650.
For the best prices when booking domestic flights using EgyptAir's website, always change your home location (at the top of the webpage) to Egypt. Prices will then show up in Egyptian pounds, and they are often half what the same flight costs when using the website with a home location outside of Egypt.