How do I make a cookie "log"?

Just as Gammy said:
I take a sheet of baking parchment (I have pre-cut sheets, 12 x 16 in., but cutting sheets from a roll will do). In my case, I smear a thick strip of cookie dough about 2 (or 3) inches from the 12" (short) end leaving a border at the sides that has no dough. Put the end over the dough, even out the thickness across the strip with your hands, and start rolling. You want a dough-less border at each side. Keep rolling and until you get to the end. (You can cut off the excess parchment, or cut smaller rectangles, so as not to waste it) Twist the ends or press them in, wrap in plastic wrap and/or put the rolls in a zipper bag. Make multiple rolls if you like, so that you can bake smaller batches if you want to. Sometimes I'll cut a roll in half and put half back in the zipper bag and into the freezer.

How do you make a cookie log with parchment paper? Take a piece of parchment paper 4-6 inches longer than the length of the log you wish to make. Drop cookie dough into a rough log shape down the length of the paper, except for the 2-3 inches at both ends, laying the dough about 1/4 to 2/3 in from one side. Fold the larger side of parchment over the dough and push the dough into the log shape, refining as you go. When you have the log to the diameter specified in your recipe, wrap up the roll with the parchment on the long sides and tuck in and under those 2-3 inch ends. Harder to explain than to actually do. Think of a chef making a sushi roll. Maybe someone can find a video that demonstrates this better....

Kelsey,
Yes, you can make a log on a floured surface then wrap. I like to wrap cookie logs in parchment and tie the ends with twine or ribbon. I keep a few different types in the freezer, they are a perfect last minute gift.