Are you sure that you want to use Win API directly? One of the main advantage of WinForms is that it abstract the API so you almost never need it.
I think that you can uses WinForms classes like
Screen Class[
^].
Otherwise, you need to properly configure your project options to link the appropriate libraries. By the way, using 2 technology might cause some conflicts so you might need to uses distinct precompiled files or distinct projects and properly adjust compiler and linker options.
I would recommand to uses a separate DLL for the stuff that access the API if your application use the API a lot as it should help minimize conflict and improve the maintainability if you decide to not use the API directly anymore in the future since those calls would be isolated.
In pratice, you should very rarely need to use the API directly in typical WinForms applications particulary for common stuff like GDI.
Neverthless, the following links might help you :
http://msdn.microsoft.com/en-us/library/9z5820hw(v=vs.110).aspx[
^]
http://msdn.microsoft.com/en-us/library/System.Drawing.Graphics(v=vs.110).aspx[
^]