I think your question is much to vague for a really good answer in Q&A, but I'll give it a try.
1) Copy all the IIS settings associated with the application pool and web application for your service application.
2) Make a backup copy of the sql server database in question.
3) Make sure the correct version of IIS and SQL Server are installed on the new server.
4) Create a web application and app pool for the application on the new server using the settings copied in step 1.
5) Restore the database to the sql server database installed on the new server.
6) Update your connection string in the web application so that it can connect with the copied database.
7) You should be good to go.
One way to do the transfer from IIS may be to use:
WebDeploy tool[
^]. I haven't used it myself, but is has been suggested in other forums, etc.