The process by which Pope Shenuda's successor will be replaced can be found here.
The highlights are as follows:
Following Shenouda's death, the eldest member of the Holy Synod's archbishops will become acting pope until a new patriarch is seated. If the eldest archbishop, Anba Mikhail of Assiut, who was consecrated in 1946, declines to undertake the role, Archbishop Anba Pachomeus of Beheira, who was consecrated in 1971 and is the second eldest member of the Holy Synod, will become acting patriarch for two months until a new pope is elected.
The candidates are nominated through the Holy Synod (the highest authority in the church, comprising 120 archbishops), the Monks Synod, Melli Council members, dioceses, and members of the Coptic Councils in the People's Assembly and Shura Council.
According to Coptic Orthodox tradition, the pope is elected by a number of processes. Candidates, chosen among monks and archbishops, must be at least 40 years old and have been monks for at least 15 years. Following an election, the names of the three candidates with the most votes are written on pieces of paper and placed in a box to be picked by a child — not more than nine years old — whose eyes are closed.
The thing that I find fascinating about this is the element of the Holy Spirit, whose hand is forced into the selection process. (In the podcast "How to Do Everything?," the Yale Divinity Professor says this is the stated aim.)
In Ancient Israel, The Urim and Thummim were cast (essentially drawing lots) for things like this, and when the Disciples wished to replace Judas, they did the same thing.