I am curious to know who the copyright holder to a manga is: is it the mangaka, or the publisher (such as Kodansha, Shonen Jump, etc)?
Who do you have to contact to obtain a license for streaming it?
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As I mentioned in my answer over at How is an anime based on western-literature made?
Usually if somebody wishes to obtain said rights, they would hire a lawyer, as obtaining the rights, setting the terms and options, and the costs that come with it are surrounded by a lot of legal rump slump
But this depends quite a bit on what your 'end goal' is.
I would advise the above in almost any scenario, as the lawyer can keep you 'save' can help you set up the license, prevent loopholes, etc.
However, if you prefer not to use a lawyer, or find it too much of a hassle/ expensive (in which case you might just stop here, a license does not come cheap) you can use the following steps to obtain it:
Determine the copyright licensing company
LoganM's answer on finding reliable information regarding licenses for anime/manga is a good starting point to determine this.
Call the copyright owner to order the copyrights
Take note that it might take a few calls, as the 'mentioned' authority may not be the authority to give you a license in the country you wish to stream from/live in.
Complete payment, and store your license somewhere safe
Retain paperwork from your copyright licensing in your files to enable you to prove that you purchased a license for the public showing.
For some more 'detailed' insight in these actual steps, you can take a look at the Anime News Network post which covers the above points quite in-depth.