I using Visual Studio 2010 (.NET 4). I need to create a COM object (in C#) and have no idea how to get started (what type of project to use,etc.)
You could use a class library project. Declare a type with methods that will be exposed as a COM object.
Make sure that the assembly has been made COM-visible:

And finally register it using regasm.exe:
regasm.exe /codebase mylib.dll
Now the assembly is exposed as a COM object and the type you declared can be consumed by any client that supports COM.