By creating the user, you give them access to the database. However that does not give them access to any objects (tables/views/stored procedures).
For that you need to give rights to objects. What I suggest is you create a role in the database, add the user to the role, and then use the GRANT (or the dialog in SSMS) to give rights to objects.
Is this for a regular user to access the db, or a developer/power user? There are some built in roles for reading and writing to all tables.