I would volunteer to be the leader for the round, so my strategy will be taken seriously. There are no easy tricks to this, just skills. Take this as the sport that it is, while the opposing team thinks it's just a children's game.

The TV show got a few things right and some things wrong. There are no benefits to standing on different sides, just stand on the left since most people are right-handed. Lean way back, but make sure you can still apply the strength in your legs. Place the big guy at the back, he's the Anchor, and slightly wrap the rope around his waist and shoulder. Don't try to make the opposing team fall, it doesn't work, and never walk forward trying to accomplish that! If you or your own teammate falls, just get right back up without breaking formation; flat down, straight up, use the rope, no turning, no giving up.

Now the most important thing is the friction of your feet to the ground. Most shoes just doesn't stick well enough. Have your whole team secretly take off their shoes separately so the opposing team doesn't notice and copy you. Explosively pull the rope at the same time as a team, following the same rhythm; chant "pull!" roughly every half a second.