1. From any app that can save/save as files, choose File->Save or File->Save As...
2. If the application that opened the dialog suggested a filename, it is selected in the filename entry box.

I would suggest to replicate Nautilus' "rename file" behavior: If the
application that opens the dialog suggests a file name with an extension,
select only the file name and put the cursor between it and the dot.

Since Bug #468445 was fixed this would allow the user to simply type a name of their choosing, replacing the default, and leaving the extension intact. It's easy enough to change the extension then, if wanted, which is a less common operation than deciding on a name, especially for Save As.