It is represented by a red and white Yin and Yang symbol in the center of a 5-pointed gold star in ODST and Reach. In Halo 4 it is represented by the same yin-yang symbol set inside a red pentagon set within a larger grey pentagon.
It is awarded exactly the same way 'assists' are given in traditional multiplayer; damaging an enemy and having him finished off by someone else. It is also a fairly common medal in 4-player Firefight. To gain an assist in Halo: Reach you need to deal at least 40% damage to the enemy.