I was having issues compiling the sample c# projects as well.
Looking at the build events, I see a pre-build event the executes the CopyFileGDBAPI.bat script, and I can see the dlls in the bin directory after I build the project. Unfortunately, I was getting this error message
"Could not load file or assembly 'Esri.FileGDBAPI.dll' or one of its dependencies. is not a valid Win32 application"
So I made sure I the solution and all projects were x86, and then tried to debug it again.
I also read the ReadMe.txt file to make sure I wasn't missing anything.
The only way I can get the project to compile, is by adding a the FileGDBAPI.dll to the project, and have the dll copied to the bin directory.
So this was my last resort, posting a question on this forum after hours of wrestling with it.
After I posted this question, I was able to find an earlier posting that mentioned the FileGDBAPI.dll had to be in the same directory as the executable.