How to move (and overwrite) all files from one directory to another?

It's just mv srcdir/* targetdir/.

If there are too many files in srcdir you might want to try something like the following approach:

cd srcdir
find -exec mv {} targetdir/ +

In contrast to \; the final + collects arguments in an xargs like manner instead of executing mv once for every file.

mv -f source target

From the man page:

-f, --force
          do not prompt before overwriting