Before the war
At one point, years before the event of GTA San Andreas, the two hispanic gangs had a misunderstand, making the both gangs as bloody rivals.
Beginning of the war and decline
At the beginning of the game, the Vagos were too much stronger than the Aztecas, having control of northern and eastern parts of the South Central of Los Santos meanwhile the Aztecas occupied the southwestern of South Central. Later on the game, the gang leader Cesar Vialpando left the city of Los Santos with Carl Johnson, the Ballas and their allies the Los Santos Vagos had taken over all the gang territory in Los Santos. When the two returned the Vagos had taken over all of the Varrios Los Aztecas territory.
The end of the war
Then in the mission Los Desperados, Cesar, Carl, and the three high-ranking members of the Varrios Los Aztecas (Sunny, Gal and Hazer fought with the Vagos throughout the El Corona Village, starting from the train station and ending at Cesar's house. It was a very big shootout between the two gangs, leaving serious of Vagos' members dead and the Varrios having control again of El Corona.
Here's a video of the most important point of the war, as depicted in the mission Los Desperados.