Zotero

Zotero styles are written in an XML language called CSL (Citation Style Language) which is also used by other citation managers such as Mendeley or Papers. To modify a style, there are 2 tools available :

• The style editor in the Cite/Styles tab in the Zotero preferences
  
• The online editor

You may prefer the online editor if you are not very comfortable with coding, but the previsualization works with a limited number of item types.

• You need to change the name of the style; this will prevent your changes from being deleted the next time the style is updated in the official repository.
• Change the name in the "info" part of the style: change the title, the link, and the identifier <id>.
• Then you can save it on your computer( CSL Editor's Style menu-> Save Style)
• Then install it in your Zotero: Zotero Preferences -> Cite -> Styles -> + button under the list of styles, and select the csl file on your computer.

You can request a style if you cannot/do not want to write it yourself. You should only request an existing style, e.g.  the style of a journal, and provide a link to the online documentation.

Or you can create it yourself (if you have the time and the motivation). First, find a style that is close to one you want to create (Search by Example in the CSL Visual Editor) and make the necessary modifications. 

If this style is an "official" style, you can have it validated, and it will be available to other users in the style repository. There is first an automatic validation to check for errors, and then a human volunteer validation. The best way to do is to create a pull request on GitHub.