Alexandria Port is about 20 to 25 minutes from the airport by car. Turn onto Mohammad Fawzi Moaz when you leave the airport, and go northeast. When you reach Smoha Square, use the fifth exit. When you get to Al Ibrahimeya Square, follow the first exit to El-shaheed Gawad Housny. Using the third exit at the traffic circle, turn onto Abou Quer and go across the Suez Canal Bridge. Take a left at Estanbol-Salah Moustafa, then a right onto El-horeya Rd, which turns into Fouad. Turn right at Salah Salem, which becomes El-shaheed Mostafa Hafez. Go left at El-nasr, take the second traffic-circle exit and turn right onto Al Bitash. A left will take you to the port.
For more info, see Alexandria Port Guide