There are several ways.

I'd start by exporting the data.

So in Studio Manager setup both databases, the original and the new.

Right click on the old database and left click on Export (or Tasks -> Export, I can't remember)

Choose a destination being the new server and follow the wizard. Tick all tables when they appear.

SQL Server will over drop the existing tables in the new server and recreate new ones identical the the old with the data.

Another method is to backup the old and restore it to the new. This can be a little tricky, as sometimes you need to you a SQL script called Restore FileListOnly. Look it up, it's a straight forward script.

The third and simplist method is to detach the the original database and attach it onto the new server. This literally means detach and attach, so you can guarentee it's the same database. It also means that the database will no longer be available on the old server as you have now detached it.

You still haven't said what the error message is.