Q on using shell mode remotely

["Drew Adams" <drew.adams@oracle.com>]

My question is: can you use shell mode remotely?

I use ftp through Emacs (ange ftp or tramp with tramp-default-method = ftp)
to access files on a remote box. I have Emacs running on Windows, and the
remote box is GNU/Linux.

In general, I haven't been using shell-mode, locally or remotely. For remote
use, I've been using VNC or Tarantella, opening a terminal window to use a
shell - I haven't used Emacs remotely, except to edit files and such.

I thought I'd try to use Emacs shell mode on the remote box, so I gave it a
try: I opened Dired on a remote directory (/host-address:/home/my-home). I
then used M-x shell. However, the shell opened with a Windows Temp directory
as the pwd, and the shell that was used was my Windows shell (bash). And, I
couldn't cd to a remote directory within the *shell* buffer, even using the
syntax /host-address:/home/my-home...

So, my question is, can it be done? Can you use Emacs shell mode remotely?
If so, how?

Ideally, shell-mode would somehow figure out where I was (e.g. remote
location) and use the appropriate shell when I do `M-x shell', since I
logged into the remote box for ftp. If that couldn't be done automatically,
I could tell Emacs what shell to use for remote use.

Is anything like this possible? How do others use Emacs remotely?