There are a total of six different Co-Op missions. Completing them is simple, but earning a gold medal will require a good team and coordination. You will need at least two players to start a match, but four is suggested.
Your overall score and time will factor into how well you do, and what badge you earn. Play as a team, don't run off and make sure that you score high enough points.
You must have all your players alive at the end of each mission. All the missions are fairly simple, though "The River" will probably be the one mission which causes the most trouble. If a player quits mid game this will damage your overall score.
If you make sure you complete all the objectives within a timely manor, and all players are alive at the end you shouldn't have any issues with earning each gold medal.
The Kidnapped Girl
I suggest you play through each mission a few times to get used to the objectives. Most are simple and require little effort, the faster you complete each mission the more XP you will earn from extra side objectives.