Transport in Egypt is not a problem. Taxis, buses, trains and flight services are all at your disposal. Travelling by taxi is cheaper, while buses are the most convenient and preferred transport. Buses can be booked from https://go-bus.com/
Travelling by plane is a good option here. Egypt Air is the national carrier and has a lot of regular flights taking off and landing on a daily basis. Egypt's air services are quite up to the mark, connecting a lot of towns to each other fairly quickly. Luxor, Alexandria, Aswan, Hurghada, Sharm el-Sheikh, Abu Simbel, Marsa Matruh and Marsa Alam are some of the places you can get to by air.
The Egyptian National Railways operate in Egypt. The train services are frequent and regula, with the Cairo to Alexandria route being the most popularly travelled. There are also overnight rail services which are run by private companies, taking you to Aswan, Luxor and more.
Egypt has a very convenient bus system. Its network is widespread and this mode of transport is very commonly used. Pullman, West Delta, El Gouna are some of the government bus companies that are popular and serve a lot of routes. You can also travel via taxis. They are definitely cheaper. Hiring a taxi for one day would cost you about EGP 100-200.
The ferry services that used to operate from the Red Sea resort area to Sharm El Sheikh and Hurghada are no longer operative.