Need to create join on multiple ids on same cell
WARNING, this violates some basic database design principles. Like @a_horse_with_no_name notes, you want separate values (user names, user IDs) in separate rows / columns, not aggregated in a single comma-separated field. IMHO this is the most important reason you're not succeeding in writing this query on your own; otherwise, some simple JOINs would suffice.

But, if you insist, it can be done. Here's an example, using the STRING_SPLIT function from SQL Server 2016 to split comma separated strings and this trick to join them again:

SELECT file_name, LEFT(ca.value, LEN(ca.value) - 1), assign_users_id
FROM files AS extern
CROSS APPLY (
  SELECT user_name + ','
    FROM files AS intern
    CROSS APPLY STRING_SPLIT(assign_users_id, ',')
    INNER JOIN users
      ON users.user_id = value
    WHERE intern.file_name = extern.file_name
    FOR XML PATH('')  
) ca(value)
GROUP BY file_name, ca.value, assign_users_id




SQLFiddle