USE DatabaseName
CREATE USER username FOR LOGIN username
GO
EXEC sp_addrolemember db_owner, username
GO

For read-only access you would want to use db_datareader role instead of db_owner. For read and write (but not changing schema, etc.) add it to both db_datareader and db_datawriter

Or, if you need more fine-grain control you may specifically GRANT/REVOKE/DENY select/insert/update/delete permissions on tables or views and/or exec permissions on functions and stored procs:

USE DatabaseName
GRANT INSERT ON table_name TO username