Team Fortress has in most cases two teams, blue and red, there are many different games that we can play in one of the teams.
Games
Capture the Flag
One of the games if Capture the Flag where as everyone knows the point of the game is to capture a flag. In this game, you must capture a brief case called ''the intelligence'' back to your base before you get killed by the opposite team. The way of getting ''the intelligence'' is by somehow sneaking into the other team's base, getting into the run where the intelligence is hidden, make your character go over the case, and it will send out a general message that the intelligence has been stolen. Now, it's the time of destiny, you must run back to your base and go into the room where YOUR intellingence is hidden, get close to your intelligence and it should send out another general message saying your team has captured. The game will add your team a point, all games usually last until astleast 4 captures your team or your enemy team has made.
Control Point
The point of Control Point is to capture all control points by making it your team's. The way you do that is by standing on in for an amount of time until the timer goes off saying that the command point is now yours. But, you must also get threw team red, who will be defending, or if you are team red, then don't let blue stand on those control points.