Newbie SQL Permissions Request

I am not a DBA and am a beginner at SQL.
We have a client running SQL that needs to grant permissions to a DB to a specific user.
The DB does not appear in the list of DB's available for connection for this user.
Here is the request from the user:

I just finished writing a Crystal report that utilizes data from both databases (PRODUCTION and unipoint_Live) to measure our suppliers’ on-time delivery performance, quality performance, and combined score. This is something we must do for AS9100 compliance and has been (until now) a manual process.
The report pops up to ask for a username and password when trying to connect to the uniPoint_Live database.
The folks at unipoint have advised that this may be because the username support (which is already utilized for JobBOSS reports) does not have permission to see the unipoint database.
They recommend that the user be able to access both databases for situations like this.

Any input is appreciated and thanks for understanding.

Are you in a windows environment with active directory meaning you have each login user and password?

This means that user doesn't have access to the database either. You would need to know the user name that the user is logging in with. If you don't know it, you can look in the SQL logs (SSMS Management>SQL Server Logs) to look for a Login Failed error. When looking at the log, you can choose filter and pick source = 'Logon' to show the errors. This will give you the login errors and should point you to the user they are using. You can add this to the database with the db_reader role