Obviously you will need to upload your database onto catalyst2's servers.
SQL Server Hosting Toolkit - Home is an easy way of doing it. Generate a SQL script from your local dev copy, and then run the script on your database. Job done.
In terms of connection strings your just changing the host, username and password. The only possible real difference here is that you might be using windows authentication with your database whilst Catalyst2 uses SQL authentication. The difference can be seen at
ConnectionStrings.com - How to connect to SQL Server 2005 with windows authentication being the trusted connection and sql authentication being the standard one.
If you need any further help, shout up.