You can get cygwin from http://cygwin.com/

Follow the instructions to install by downloading and running
setup.exe.  In addition to the default packages, you should select
(at least):

bash              (in Shells)
openssh           (in Net)
rxvt              (in Shells)
vim (or emacs)    (in Editors)  (also best to get emacs-X11)
xinit             (in X11)
xorg-server       (in X11)

This is done by clicking on the small icon (sort of an oval
with two arrows) until it tells you a version number, which
it will then install.  Cygwin will automatically include any
other packages on which a given package depends.

You can always rerun setup.exe and select additional packages.
For example, it is handy to have xclock (in X11) and the X11
version of emacs called emacs-X11 (in Editors).   You can also
install gcc (in Devel), which will allow you to compile simple C++
programs such as the ones we'll see in the first two problem sheets.
(But after that we will need packages such as ROOT that may be
difficult install on your own computer.).

Once you have gone through the intsallation it will put an
icon on your desktop for cygwin.  This does no harm, but it
is not what you want.  What we need is an xterm, which is a
terminal that uses the X11 windowing system.  To get this, go to

 start -> all programs -> Cygwin/X -> XWin Server

This will start up the Xwin server, which you can tell because there
will be a small X in your taskbar.  It can  basically stay running,
but if you want to kill it later, right-click and exit.  In
addition, starting the Xwin server by default also starts an xterm,
which is OK but appears not to have a scroll bar :-(.

From here you can do, e.g.,

 ssh -X username@linappserv0.pp.rhul.ac.uk

to log into the RHUL linux machine.  From there, try e.g.

 xclock &

and see if it opens up a separate window with a small clock.

If you close the xterm, the X will remain in your task bar.
You can go to

 start -> all programs -> Cygiwn -> rxvt-x

which will open up a slightly nicer xterm, which you may prefer to
use rather than the one that is opened when you start XWin.