How does a series go from manga to anime? In a previous question, I asked about Dragon Ball Super being released before its manga. My question here is about the life cycle of a manga becoming an anime. 

From my understanding, an artist or mangaka creates their comic called manga and it gets published by a major studio if it's deemed worthy. From there if it cultivates a big enough fan-base it becomes licensed by a studio like Viz, Funimation or Bandai. And from there it becomes a game, movie, t-shirt, toy, etc.

Is that the way most anime's come into play? If not, what is the proper life cycle from drawing to manga to anime?
Anime might be produced based from many types of different stuff, not limited to manga, but also other stuff, like light novels. There are also some anime that aren't based on any manga.


  From my understanding an artist or mangaka creates their comic called manga and it gets published by a major studio if it's deemed worthy. 


Yes, this is pretty much correct. The mangaka can release their own manga too, but it is less likely to be as popular.

The mangakas usually work together with magazines like Jump where they have someone they can show their ideas, drawn simply. If their idea gets accepted, they start on producing it with more details.


  From there if it cultivates a big enough fan-base it becomes licensed by a studio like viz, funimation or bandai. And from there it becomes a game, movie, t-shirt, toy etc. 


Yes, this is also correct. The mangakas license their manga with some companies to make it an anime, and swags of it.

I really recommend you to read the manga or watch the anime of "Bakuman." which tells the story of 2 teens producing manga (and aiming to get one produced into an anime), with very good amount of details on every part of the production cycle.