Chubba: I'm an American. No, I'm not proud
A bowl is typically about .25 grams to .5 grams, and refers to both a measurement of the weed itself and the pipe, as the two go hand in hand (as in, a bowl is a part of the pipe, or a bowl's worth of weed). Some people will naturally pack more in a bigger bowl, and I've even heard someone refer to 2 grams in a very large pipe as a bowl.
It is up to the owner of the weed as to how he wants to pack it. Some people like to take a few little chunks and fit them together in the bowl. Some people prefer chopped up bits that they can stuff in the bowl. Others just crack off a piece of a nug that fits more or less and cram it in. I prefer the first two methods as the last one burns shitty.
Owner takes the "green" hit, or first hit (cause the unburnt weed is green.) He can pass himself off to be nice and let someone else have the first hit. Around here, the first person to hit always lights half the bowl, saving half of the green for the next person, but these types of practices are nowhere near standard and change from town to town, state to state. Some ignore the green concept altogether.
Take a hit off the pipe, send it to the left or the right. I've always preferred the motto "right is wrong", so I send it left. It goes around until it's ash, and the next person who wants to pack some can go ahead.
For bongs, you still pack a bowl's worth, but it only makes it through about two to four hits and then it's gone. I prefer pipes myself. Double hitting a bowl isn't cool (as opposed to a joint), and there are all sorts of chances for the inexperienced to mess up and look silly (like flipping weed in the bowl when one side is ash and dropping it, or coughing and blowing weed out of the bowl).
Not much else to say... except... i love.. weed!