Build means compile and link only the source files that have changed since the last build, while Rebuild means compile and link all source files regardless of whether they changed or not. Build is the normal thing to do and is faster. Sometimes the versions of project target components can get out of sync and rebuild is necessary to make the build successful. In practice, you never need to Clean.
Build or Rebuild Solution builds or rebuilds all projects in the your solution, while Build or Rebuild <project name> builds or rebuilds the StartUp project. To set the StartUp project, right click on the desired project name in the Solution Explorer tab and select Set as StartUp project. The project name now appears in bold.
Compile just compiles the source file currently being edited. Useful to quickly check for errors when the rest of your source files are in an incomplete state that would prevent a successful build of the entire project. Ctrl-F7 is the shortcut key for Compile.
All source files that have changed are saved when you request a build/rebuild, so you don't have to save them first.
When you run your executable (F5 or Ctrl-F5), Visual Studio saves all your changed source files and builds anything that changed, so you don't need to explicitly do those steps every time. This allows for quick "trial and error" debugging.
Incidentally, if you like those little Visual Studio keyboard shortcuts, you can download posters of the C# and the VB.Net ones, respectively (I am personally a big fan of using keyboard shortcuts :) ).
Visual Studio 2010
http://www.microsoft.com/downloads/en/details.aspx?FamilyID=92ced922-d505-457a-8c9c-84036160639f
Visual Studio 2005
C#: http://www.microsoft.com/downloads/details.aspx?FamilyID=c15d210d-a926-46a8-a586-31f8a2e576fe&DisplayLang=en
VB.NET: http://www.microsoft.com/downloads/details.aspx?FamilyID=6bb41456-9378-4746-b502-b4c5f7182203&DisplayLang=en
