The Telephone system in Egypt is overloaded and antiquated. 4/5 Star Hotels will have direct line dialing and international service. Most hotels have WIFI, some offer internet access for free and some charge per hour.
Calling cards through an International Operator (AT & T etc) or credit cards can be used for calling. They do have calling cards available for sale everywhere to be used to rechage your cell phone for international calls.
There are Internet Cafes in all the major cities - Cairo/Luxor/Aswan/Alexandria/Hurghada,
They usually range from $3 to $6 US an hour, with a minimum 15 minute charge. However, the ISP's are not as reliable and it is sometimes difficult to get on particularly in the evening, and it's not unusual to get booted off.
Cellphones are everywhere in Egypt, it has one of the highest usages for cellphones in the world, which makes sense as their Telephone system can't keep up with the regular phone requirements. They have international cellphone service, and it covers just about everywhere, even the most remote areas. Outgoing calls are quite expensive, but in most cases there is no charge for incoming calls. If renting independently, check all the charges ahead of time.