Yes, Fred76 has a nice description. I call it all a dance, from the light rocking and swaying to the full body push-pull using every (well it feels like it anyway) muscle in my body. Been doing the dance for 50 years. I love doing real climbs on fix gears.

I do two things that run a little counter to the usual thought. Ride the drops anytime I have headwind (and see to it that every bike of mine is right, out of the saddle and in the drops; this comes before I locate the brake levers. I like handlebars with "sloped shoulders" like the track/pista bars and the old Cinelli 65s because they don't bruise my forearms while I do the rock. And I like fix gears set up with real reaches so I can pull myself forward, in part to get weight off the downstroke and provide a very comfortable pull on the bars to offset the hamstring/calf upward pull. I can actually do real climbing and give my chondro malacia knees a break.

If my wind is coming up too high, I pull forward and back off. That downward force from my arms is just a force. I'm not moving anything so there is no energy spent. (Energy - force X distance. Going up stairs take energy, Standing there on the same muscles doesn't.) So, hill grade allowing, I can loaf going up long hills in big gears out of the saddle. (But it does take strength! Those muscles will feel it.) When I was commuter strong and in my early 50s, I loafed up Portland's Germantown road on my 28 pound winter fix gear with racks and fenders on a 44-17 gear. Yes, I was loafing with every fiber in my body on the steep hairpins and laughing about that absurd concept up the hardest stretches. This is where my super long stems really work for me; in allowing full body use but not maximum effort (and totally counter the the weight over the pedals concept).