Origin of the conflict
Ethnic divisions en tensions between Somalia and Ethiopia exist for a very long time. Already in the 16th century, an Islamic leader in Somali culture was popular for his jihad against the Ethiopians. Oral and cultural traditions fuel the tensions between the two countries.
These tensions got worse after the independence of Somalia in the 1960s. Many of the ethnic Somalis in neighbouring countries wanted to join this new state. The government of Somalia supported self-determination for the Somali people in Ethiopia, Kenya, and French Somaliland (now Djibouti). This caused tension because those countries didn’t want their land to be united in a greater Somalia.

Chronological timeframe
1960-1964: Border Dispute
Somali people live in different countries, because the boundaries were artificially drawn by the former colonial powers. The wish of some to the unification of all ethnic Somalis led to cross border raids by Somali insurgents and violence by Ethiopian troops.

1977-1978: Ogaden War
Conflict over the Ogaden region of Ethiopia.
1982: August Border Clash
The Ethiopian military supported Somali rebels, who invaded central Somalia and captured several towns. This caused the United States to give military assistance to Somalia.
1998-2000: Cross-border warfare during the chaotic warlord-led era.
The open warfare over the border caused tens of thousands of lives and sending hundreds of thousands of refugees into flight.
2006: Ethiopian troops moved into Somalian territory in July, after the Transitional Federal Government (TFG) in Somalia invited Ethiopia to intervene.
The war starts when Ethiopian troops, backed by the US, invade Somalia to help the TFG in Baidoa (city in the South of Somalia). The TFG was resisting the Islamic Courts Union (ICU) forces.
2007: Ethiopia said it would withdraw soon, but the TFG, US and UN opposed Ethiopian withdrawal, because this would create a security vacuum. The ICU demanded immediate Ethiopian withdrawal.
2009: Ethiopian troops withdrew from Somalia
The insurgency of the previous two years had lead to a loss of territory and effectiveness of the TFG. A power sharing agreement between Islamists splinter group Alliance for the Re-liberation of Somalia and the TFG has come into force. The conflict hasn’t concluded yet. A struggle between hard line Islamist factions and more moderate factions within the government still exists.

Involved actors
Ethiopia: involved because of the border disputes in the early wars. It intervened in 2006 because it faced a direct threat to its own borders.
Somali Transitional Federal Government: the interim Parliament of Somalia is formed in 2004. The four major clans are represented in the government.
Islamic Court Union: compete with the TFG to control the country. The ICU is group of Sharia Courts who united themselves to form a rival administration to the TFG. Sharif Sheikh Ahmed is head of the ICU. They are often referred to as the Somali Islamists.

Reaction of the international community
During the Cold War, the US and Soviet Union each supported a country by giving military aid in the Ogaden War. During the August Border Clash the US gives military assistance to Somalia, to act against the rebels that got support from Ethiopia. The last time Ethiopia invades Somalia, in 2006, the US (as to the UN and the Somali Transitional Federal Government itself) oppose the withdrawal of Ethiopian troops. They are afraid this would lead to a more unstable situation in Somalia.

Sources
Abdinur, Mustafa Haji (2006-12-23). "Somali Islamists give Ethiopia one-week deadline to withdraw troops" Agence France Presse (http://www.reliefweb.int/rw/rwb.nsf/db900SID/VBOL-6WEFKC?OpenDocument).
BBC Timeline http://news.bbc.co.uk/2/hi/africa/6159735.stm.
http://en.wikipedia.org/wiki/Ethiopian-Somali_conflict.