back up and restore SQL Server 2008 DB on another server problem?

I'm moving SQL Server databases from one server to another. I don't think I can get direct access, but that might be a possibility. I did what I've done before in the same network, which was:

* backed up the database

* Transferred the backup

* Created a new blank database on the new server

* Restored the backup of the DB with the same name.

It says backup successful, but when I want to explore the tables in Sql Server Management Studio, it won't expand the database to show me the tables, etc.

Message is "The database [db name] is not accessible (ObjectExplorer)".

If I try to view properties, I get an error message with more info. It says,

"The server principal [my domain\username] is not able to acccess the database [DB name] under the current security context. (Microsoft SQL Server, Error: 916)

I believe it's because I have different accounts on the two computers, and they aren't on the same network. What can I do? Is there some way I can add permissions to the source database before backing it up or something? I'm not really a network or DB guy, but I am a developer so I can figure out a technical explanation if you have one.

Thanks in advance!