Greeting Murat,
The easiest rout is to go to Egypt on a tourist visa, check to see if you need one in advance or whether you can get it at the airport (most countries can) and then aply for a work permit and residence permit at the Mugamma Offices on Midan Tahir (near the Nile Hilto) in Cairo.
It is supposed to be a long, drawn out, beauraucratic nightmare getting these permits and be warned, if your residence permit is turned down, you will not be able to find out why, no apeal, and you will be asked to leave the country and will find it dificult to return. There are many people happily living there on tourist visas which they renew. The authorities seem to prefer this as if you are naughty they can tell you to leave whereas if you have the full residence permit it becomes impossible to do that.
I'm not quite sure whether you mean to do some time studying or hoping to find a teaching job in Egypt. There are two excelent universities in Cairo, the American University in Cairo and Cairo University. You may prefer Cairo University if you want a taste of true Egyptian culture. If you want to study there then you should have no problem with visas and plenty of time and good contacts to gert residence and work permits together. If you get a job teaching then you should have a lot of help sorting it all out.
You'll find that there will be many Turks living there. Hang out at a few coffe houses and ask around in them and you'll soon meet up and will get all the info and help you require.
Rob