How do I find out which dlls an executable will load?

There are utilities that will do this for you.

In the past I've used the MS tool (depends.exe) that came with (I think) VB.:
VS2010 VS2012 VS2013 VS2015 Current

and there's this as well:
http://dependencywalker.com/

and probably others as well.

dumpbin is a tool that comes with VC++.

To see what DLLs a program will import:

• Open Visual Studio
• Menu Item Tools | Visual Studio Command prompt
• cd to folder containing executable
• dumpbin /dependents whatever.exe

Dump of file whatever.exe

File Type: EXECUTABLE IMAGE

  Image has the following dependencies:

    AIOUSB.DLL
    sqlite3.dll
    wxmsw293u_core_vc_custom.dll
    wxbase293u_vc_custom.dll
    KERNEL32.dll
    ole32.dll
    OLEAUT32.dll
    MSVCP90.dll
    MSVCR90.dll

To see what functions (and DLLs) it will import, use

C:\> dumpbin /imports whatever.exe