How do I move my SQL database from my old web host to my new web host

I have a database installed from a program in a book. Initially installling it and getting it working fine.  Now 9 months later a new host has bought out my original host and now nothing is working on my web site as a whole and the company who bought out the first host has given me so many problems that I have decided to move to another host.  The new host that bought the old host has given such bad support it is unreal.  So, here is my problem I am ditching my current (very bad) host to a new host and I need to move my SQL data and database.  It seems that I can generate scripts that would get all of the database components into a scripts, but the data is not scripted to carry over.  I read other posts like this one where the person who provided the solution state create the database and restore a .bak file.  I tried to do this but it seems it did not work for some reason, maybe because the main database names are not the same or something.  So I am here to get answers from experts like you.  I am a very knowledgeable programmer but some what a novice to Microsoft SQL server.  I need an answer quickly.

Tony...