Use the shortcut SPACE f f to open Helm Find Files:
Type in the name of the new file and press enter:
Type y to create the new buffer, and SPACE f s to save the file:
Your new file is created!
If you click away from Spacemacs, and can't type anymore in the Helm mini-buffer, use SPACE w b to get your cursor focus back.
Next: How can I switch between files (buffers)?