What is the process like renting an apartment in Egypt

you are welcome 
about renting , deposit depends on sharing  flatmate or renting  your own apartment 
,if its about sharing a flat  ,  most of  them  doesn't ask for deposit  , it will be about the monthly rent and extra fee
fee usually include (   bawab , cleaning ,  internet service , electricity )   it will be  around 300 L.E as average rate

if you are going to rent your own  apartment  ,  just dont make things complicated , and pay the deposit  according to how long you will stay  , with minimum rate equal to one month of the rent
, so you  staying  year or less than , pay  a deposit equal to one month , 2 years =  2 month  and etc.

extra fee still around the previous range  , according to the utilities available in the place 

other procedures like contract  ,you will find more easier than to discuss

Thank you Wal-83, very helpful.

Hello and welcome to Egypt in advance. I am Egyptian living in the UK currently but will be soon back to my home country. In terms of renting, you can start by narrowing down the area where you would like to live. Try to pick it up close to your work place as traffic in Egypt is very difficult. Then you can try to use a "semsar" or broker. If you know a few people there, maybe your colleagues at work, they can also put you in touch with a few "bawab" in the neighbourhood, those act like building guardians but often know about flats available for rent. In any case, if you decide to go for Maadi in Cairo, let me know as my Dad has a nice 2 bedroom flats that he rents to expats. Let me know if you are interested and  can send you some pics. Good luck!