The Constructors' World Championship is based upon your teams total points. For example, if you win the first race and your teammate comes second, your Constructors total would be 43 (25 +18). In order to be awarded the Constructors' title, your team must be on top of the Constructors' table at the end of the season. I suggest setting the difficulty to easy and winning every race. Even if you have a terrible teammate, winning all the races should be enough for you to clinch the title.
If you're having trouble, try accepting a contract offer from Ferrari, Red Bull or McLaren, as those teams have some of the best drivers.