What’s the best way to target multiple versions of the .NET framework?

You will at least need one VisualStudio Solution with 2 projects (one for .net 4 and one for .net 4.5).

Add all codefiles to the .net 4-project and in the other project you add the code files as link (use "Add Existing Item..."-Dialog and chose Add as link)

Now you add all codes and classes for .NET 4.5 to your 4.5-project.

Additionally you should define your own compiler switches (conditional compilation symbols) to your projects. Like NET4 for your .net 4-project and NET4.5 to your .net 4.5-project)

You set the switches in the project settings under Build->General->Conditional Compilation Switches

In your code you can use the switches as follows to generate code for .NET 4 or .NET 4.5

#if NET4
  // code only for .NET 4
#endif

// code for all framework versions.

#if NET45
  // code only for .NET 4.5
#endif