Player's League Advancement

In the Player's League in chess.com , how to you advance into the next league ? For example, I am in Wood League. Then how to I advance to stone league? Hope you got to understand my question.

www.chess.com/leagues

I know that but I could not understand this meaning:
Finish at the top of your division to move on to the next level

Can you kindly explain me?

In the link provided it tells you,

Your in wood league so top 20 get promoted every week. 

Everyone is randomly assigned to a group of 50 players called a division. You get trophies by winning games.  At the end of the week, they look at the count. The first week, where you are, the top 20 move on...

Thank you. Now I understood my question. Also thanks to @StumpyBlitzer

Is there a minimum number of moves that must be played to get a trophy for a win? I've noticed two wins of mine... a resignation and a fool's mate didn't show me receiving a trophy.

Minimum is 10 moves.

I also have a same question. My opponent resigned. But it did not show any league points.

Please make other names for leagues, I don't want to be in Stone League. 

I like this new league,, it's just give me another goal to achieve everyweek

this is confusing as I didn't think you could resign before move 10. I also understand that rigging games is possible, but if I checkmate in less than 10 moves I want that to show as a win! 

You can resign at any point, unless you're playing an arena. That requires at least 10 moves by both players.

Iv'e been playing in the league and i have advanced to silver but i have noticed on a number of occasions that the league doesn't add up the points correctly.  Take today for example:  It's day 1 and today i have 20 wins and 1 draw all on rapid games so that's 305 points right?  Apparently not, according to the league table i have 270!!! I seem to have lost 35 points somewhere and this isn't the first time.  Anybody else getting points dropped randomly?

I guess this could have been a hard-resignation (threw computer in the river).

Sure, a useless goal is better than no goal...

I am very much enjoying the leagues (automatic entry) as it gives me more incentive to play more often. Before, I hesitated to play often because every loss brought down my rating, and that's a bummer. But in the leagues, losses count for nothing--only wins. So if I play 10 games in 1 day and lose 7, I still have 3 wins--ergo, 45 points for the day. (Don't even ask about what such a result would do to my rating).  It's another way to track your progress and success aside from ratings. Go, chess.com!! BTW, I just got into Bronze yesterday.

You rematched another member multiple times. Only three of those games (in the same day) count for league trophy purposes.

https://support.chess.com/article/3176-i-just-won-a-game-why-didnt-i-get-any-league-trophies

Do you lose trophies if you lose games? Like do you go down in you're division?

No, there's currently no way to drop down or lose trophies.