Internships are almost always unpaid as the intern is gaining skills and experience. It is critical to find the right match so that the relationship is beneficial to both intern and company. Full time students have the easiest time finding internships because of their age, lack of real life skills, amount of free time, and education.
To secure an internship aboard, it is usually necessary to find a company that sets up the internship. Internships are commonly set-up through a university for its students. Some agencies require a fee to secure a placement.
If you know anyone in Cairo - get in touch! It's not necessarily what you know, but who you know. Friends and family, or any contact you have in your desired business may know of a position. There are also professional social networks which allow for people to make business contacts. You may also use EasyExpat's forums to meet other people living and working in Egypt and make business contacts.
To meet Cairo's business community the American Chamber of Commerce offers great connections.
Programs or internships through a school usually arrange a visa. Check before signing up for a project. Depending on the length of the internship, you may need to obtain a residency permit.