Two days ago I went to El-Tor to extend my Egyptian visa. This was even easier and cheaper then I thought. To start with, if you are in Sinai, take the bus from Sharm El-Sheikh to El Tor, which will take about one hour and cost around 1 euro. Then, take a taxi for less then one euro or walk 15 minutes to arrive at the place for all passport enquiries. Not so many people in this town speak English, so if you need to ask for directions you can show the note with text that I will put further down on this page (later).
At the passport office, fill in the English form which you can also find below, and leave together with a copy of your passport (the page with your photo + the page with your current visa). These copies you have to make before you arrive here, for example at the post office 500 meters away (costs 10 cent). The whole procedure at the government should take about 30 minutes and cost you 1 euro for a 1 or 3 month longer stay in Egypt. If you want to stay longer, it will cost less then 10 euro for up to a one year period.
The office is open 8 am to 3 pm every day except Fridays. When in El-Tor, take a random walking tour in this nice town. People here are incredibly friendly and the town reminds me visually more of India then Egypt.
Be aware that there are rumours in Egypt that after the new government, about a year from now, it will be more difficult to get a prolonged Egyptian visa. Also, it is possible you only will be allowed to stay for 1-3 months total within a one year period, depending on where you are from.
Things to take with you: Passport and money (maximum 5 euro in EGP currency needed)