First: even though the doctor told you yesterday that you can dispense with the sling... put on the sling. On your bad arm. Um. Yeah, but the jacket goes on first, and then the glove on the to-be-enslinged hand, as the glove won't fit otherwise.
Second: assess the snow. Establish goals, but be willing to modify them as your body dictates.
Third: contemplate your navel. It will play an important role.
Fourth: place the handle of the snow shovel against your belly, right about at your navel, or a bit before. If possible, endeavor to have sufficient poundage such that you have an adequate roll just above the belt line. This will help keep the snow shovel in place.
Fifth: use your body weight to push the snow shovel until you have a worthy amount of snow. Today, that is approximately just under 1 linear foot of dense, wet snow & sludge. Less, if you are not terribly large. Try to ensure that you get about the same amount of snow distributed across the snow shovel, or step six will fail.
Sixth: toss the snow. To do this, reach down as close to the scoop part of the shovel with your good hand as you can without bending forward too much. Bend at the knees. Do the following simultaneously: straighten the knees, arch the back (pushing belly forward), lift with good arm. Direct the momentum of the lift in the direction you want the snow to go using your hips and good arm.
At stage six, if the snow load on the shovel is unbalanced, the shovel will turn (unless you have a particularly firm and prehensile layer of belly flab) and dump the snow from where you just got it, but more spread out. Due to the dispersal, it will take two scoops to clean up. DO NOT TRY TO SAVE THINGS BY GRABBING THE HANDLE WITH YOUR BAD HAND. THIS WILL FAIL AND FUCK UP YOUR ARM AS WELL.
NOTE: keep in mind that you don't have to finish. Don't stress it; you can take a break and come back later. The snow ain't going anywhere.
EDIT: apparently Linda took pictures. Note the aikido-like stance (of which I'd been unaware).