There's a manga I like and I want it published in the West. What can I do about it?
The best way to get a title licensed is to show that there is interest in the title via sending questions/tweets, e-mails, or filling out various companies' surveys. For example, Seven Seas Entertainment has a monthly reader's survey, and part of the survey asks you which Japanese manga series and which Japanese light novel series you would like to see licensed and published. They do tally the results.

Also, publishers in the west sometimes have ties to the series of a company, author, etc. (it's case by case), so it's worth looking into whether the company can legally license it at all. For example, here are some ties:


Shueisha/Shogakukan - Viz Media
Square Enix - Yen Press
Kodansha - Kodansha USA or Vertical


See also this reddit thread and Seven Seas Entertainment's ask.fm feed.