NOTE: the life system is still work in progress. But if you wish to use the current setup, it is possible to get a simple setup going.
To set maximum player lives, you can either specify "mp_lifecount x" in the console or in a Map Config File, or set the "Maximum Player Lives" key in the "synergy_gameinfo" entity in your map.
When all players are dead, entities named "game_all_dead" are triggered.
In Teamplay games, "game_rebels_dead" and "game_combine_dead" are triggered.
When the life system is enabled for Deathmatch games, the game becomes a Last Man Standing mode, where the last player alive wins the game (since all other players are no longer able to score).
In Teamplay games, when all of a team's players can no longer spawn, the other team wins the game. This behavior can be overridden in maps if the target entity is triggered (with the name of "game_rebels_dead" or "game_combine_dead").
And lastly, when all players can no longer spawn in Cooperative games, the game is over and the next map will load. Again, this behavior can be overridden in maps if the target entity is triggered (with a name of "game_all_dead").