How to solve SIDs mistmatching in SQL or orphaned users?
There are a couple of possibilities.

First if the orphaned user is a windows login/group (type U or G) then no problem.

-- If the login doesn't currently exist on the server
CREATE LOGIN [Windows Account] FROM WINDOWS;
-- Fix the user
USE dbname
ALTER USER [user name] WITH LOGIN = [Windows Account];


If it's a "SQL Login" (type S) and the login exists then again no problem.

-- Fix the user
USE dbname
ALTER USER [user name] WITH LOGIN = [Windows Account];


If the login does not exist for a "SQL Login" then you have to create the login and that will require knowing the password.

-- Create the login
CREATE LOGIN [login name] WITH PASSWORD = '&lt;strong password&gt;';


Don't forget to make sure your password meets your windows policy requirements.
If you still have the old server you can copy the login pretty easily from the other server including the password by getting the HASH of the password from the other server. (There may be some issues depending on if the two servers are different versions).

I did a post on this here: http://sqlstudies.com/2013/03/25/how-do-i-move-a-sql-login-from-one-server-to-another-without-the-password/