Record visible just for selected users

I want to create a form where the logged author can fill a textarea and then select 1 or more system users from a checkbox

So when every user logs in he Will see that record only if he has been selected in the checkbox before.

How can i do it? Must i save values of the checkbox in a single record and then split to set the correct data set? And then how can i show the whole records to the current user as i want him to see a list of records where he is the author or where he is among the users allowed to set that very same record

I know this can be a generic request but the matter is i dont understand how i could do it, so the answer i look for is not "give me the code" but"explain me the main steps i must follow", someone can give me some hints?