How do I create a new WAD file? Does anybody know?

Yeah, open your project in WED and go to Textures (to right of Level and Presets, same place where you can use WAD textures), now right click on your wad (either on the black part or on one of your wad textures, right clicking on the title/label does nothing) and than 'Save WAD'.

I misread your question as how to save your WAD. To create a new WAD, right click in the WAD in WED and select 'Texture Manager' than select new WAD.

Then what?

Then you can add your owqn textures to it by rightclicking in the texture menu and chose add textures. Make sure your textures are in
the right format and use the power of 2 (128x128,512x512 and so on)

, if you really want to use WED, I would recommend reading a tutorial about it e.g.: http://opserver.de/doc/wed/
(it looks longer than it is)