I see lots of mention on sailing forums about standing on the bow and "pumping" the sail on a sunfish or other small boat to get going under your own power. However, I can't seem to find any videos or detailed descriptions of what this means. How does one "pump" one's sails?
You're essentially "paddling" the air with your sail. I go windsurfing in Waterton Lakes National Park, it's quite gusty there, so I've been caught a few times riding a gust out into the lake when all of a sudden the wind dies and I have to pump to get myself back to shore.
You do this by catching as much wind as you can in your sail, letting the wind take it a little even, and then abruptly sheet in, mimicking a short gust of wind. You use your boom as an oar, and "pump" in order to get a little bit of forward motion going. You see Olympic wind surfers do it a lot in low wind.
Here's a video of some windsurfers pumping their sails in light wind: Youtube - Rio Replay, RS:X Sailing.
The process would be similar on a small boat, but how effective it works for you may vary depending on your vessel and how well you can work the boom with a pumping action, be it by grabbing the boom or trying to pump by pulling on the ropes.
If you're truly becalmed, you'll likely get better results by sculling than trying to pump the sail. By hauling the tiller back and forth you can use your rudder to paddle. Start slowly and as you feel forward momentum increase you can increase your sculling rate.
Neither of these methods are as effective as breaking out a paddle however.
You literally make long strokes of the mainsheet. It is done from the stern standing. It is best with a small tail wind. Doubt it would work with a head wind.