The Mogadishu airport was bombed in December 2006 by Ethiopia to keep the Islamic Fightersfrom receiving supplies.
Jubba Airways (http://www.jubba-airways....) serves Mogadishu from Dubai, Jeddah, Nairobi, Djibouti, as well as domestically from Hargeisa and Galkayo.
It is possible to drive into the city by truck, but this is considered a risky activity, unless you employ a group of local militia which are readily available for hire. Roads link the city with many Somali locales and with Kenya and Ethiopia. Armed guards, hired security forces, and experienced guides are all mandatory for a safe entry, and even then the risk of your being injured, killed or captured is extremely high.
By ship
Small cargo ships regularly leave from the Old Harbour of Mombasa for Mogadishu and sometimes Kismayo. Speak with the security officers at the gate of this tiny port and they will negotiate a fare with the captain. The journey will take 2-5 days, depending on conditions. The sea is rough in July-August, requiring lengthier travel. Arriving by boat is risky, as there is the strong possibility of being attacked by pirates, though the port area is relatively secure.