I think you're talking about the standard standing guard pass. I've been training almost as long as you, and it was the first guard pass I was taught.
You grab the sleeve with the left hand (for example), step up to your feet left foot first. You then put your right hand on the guy's knee (left) and step back with your right leg as you push down on the knee with your right hand. That will tend to open up the guard.
Saulo has a great ground guard pass that works along the same principle.
Because you've grabbed the cuff on your left side, the guy isn't going to be able to grab your heels and sweep you that way. That's also what the "step back" with the other leg helps accomplish--in addition to breaking the guard. Saulo points out that it isn't the hand pushing down that breaks open the guard, it is the stepping back with the leg on that side.
The hardest part of this guard pass for me is after I open the guard. Our instructor has been trying to get us to drop the right leg (per this example) down over the leg on your right side (the one you "pushed" down). Knee over his upper thigh and shin pressing the leg to the mat. You want to pass over to that side. We do it by taking what I call a "backstep". The "backstep" isn't super hard to do, but I always feel like an idiot trying to explain it.