I'm confused and I can't find the answer anywhere.
How exactly does the CE work?
Example: You have General Skywalker, Mas, and Yobuck. Yobuck moves 8 squares and stops, would he get momentum when he stops moving, or when his turn ends. I think it's when he stops moving, but I want to be sure.

Example 2: Same characters as listed above. Next round, Yobuck wants to use galloping attack. Does he still get momentum, or does he have to wait until he ends his move within 6?

The CE's (as does Durge from CS the first with it) state when they "end their move". It occurs the moment they stop moving (or you as the acting player declare your intention to move no further in cases such as having remaining movement remaining, or mobile attack characters). It does not require or have any interaction with the "end of turn".

The second part of your question is answered in the wording of the CE's as well under the glossary definition of "momentum". Momentum applies only to the active turn if the character has moved at least 1 square, and does not carry over to another turn in any way.

So in short, the correct ruling, is that a character must move at least one square, and have ended it's "move" (meaning no movement remaining, or the acting player's declaration of the intention which is binding) and then automatically gains a +4/+10 from "momentum" on any attacks made at that time, or thereafter for that turn (including attacks gained from movement that can occur after regular movement has ended such as the gallop and rolling cleave interactions). It is an automatic bonus that is applied whenever the requirements have been met, and is not subject to player choice or forgetfulness (in other words, the acting player cannot ignore it in beneficial cases such as self destruct, and the opposing player is required to remind the acting player if it is forgotten).

Hope that clears it up :)