When you start a new campaign you can either join a quick match or make a private/public game where you can invite people to join or wait for people to join, and/or plugin in controllers so the party has 3 players. Once you have a full squad, complete all 5 parts of any Chapter as a full squad. They're all basically the same length so it's really just preference.
Head to the Achievement Trading Thread if you need help.
Note that if a teammate lags out during a mission, you can just wait for them to come back and proceed to finishing the mission and you'll still get the achievement. Also note that you can get this over multiple sittings, just play through to the screen where you get your score before quitting out of the game for it to count .