The art of tapping the open mouth of a beer bottle held by an unsuspecting drinker with the bottom of your bottle, resulting in a gush of foamy beer. Poor zenking results in broken or chipped bottles, zero gush of foam, and no cool points.
Johnson ran around the bar zenking people all night long. He was finally kicked out after he zenked the owner and broke his bottle.
Zenkai is the power boost that a Saiyan receives once he/she has experienced near death. In the Dragon Ball franchise, this can best be seen when Vegeta receives a large enough boost to over-power Zarbon, an enemy who had beaten him only a few episodes before.
In a much less literal definition, anyone can experience Zenkai. It's just when someone comes back stronger and better than ever from a bad L taken in life. We all have Zenkai.