Note that "solution" has a specific meaning in Sharepoint: a collection of features (like web parts, list definitions and so on) packaged for deployment as a .wsp file.
You typically build sharepoint solutions in Visual Studio and package and deploy them using some tool like Sharepoint SmartTemplates http://www.codeplex.com/smarttemplates
However in your case you already have content in a live sharepoint site which you want to move to another site. It will probably be too cumbersome to use a solution for this, especially if you want to do it more than once (though it is possible to generate a solution from a live site using SharePoint Solution Generator).
The easiest way to deploy all content from one live site to another is to create a backup of the site using stsadm and then restore it to the new site again using stsadm restore. This completely overwrites the new site.
You can move select files/lists using import/export (rather than backup/restore). A tool like SharePoint Content Deployment Wizard makes it easier to select the content to move.
