When we stir a cocktail, we're stirring something that's going to be all-alcohol. When we shake it, it's going to have some juice or non-alcoholic ingredient and that's why we want to force it together by shaking it. When you're stirring, you're just gently trying to get the ingredients to mingle; they'll mix pretty easily. We don't have to stir it like we would a cake batter or something; we're just gently gliding the spoon on the outside of the glass.
I hold it with my thumb and forefinger at the top and that part's not going to move; it's just going to hold it in place. What's going to make the spoon move is when I hold it between my middle and ring finger, and it's like a push, push kind of thing; pushing with the middle finger, pushing back with the ring, and gently getting that easy motion. These corkscrews on the bar spoon help you to make that motion. There are a lot of different bar spoons, some have deeper grooves than others. I like this one the best. It's just about personal preference.
I should say that this takes some time to learn how to do really well. I used to just practice with water and ice when I was still a bar back. About 20 or 25 seconds will get the proper amount of chilling and dilution that you want. When we're done stirring, what do we do? We strain it. That just means we're straining out the ice and leaving the liquid behind. There you go; a perfectly-stirred cocktail.