What do I need to know to be able to log into my outlook express work
e-mail account from my home computer?

debbtalk...

Most likely, the email on your computer at work is part
of a network set up by your company, and is separated
from the internet by a router and other kinds of
firewalls.

To access your work account from home, you would have to
log on to your company's network, which would require
that you have permission to access it from home, and
that you are given the technical data for how to 
accomplish this. For obvious security reasons, it
is highly unlikely that your company would be willing
to do this.

sublime1-ga

You may be able do do it with this www.mail2web.com

There are several ways to access work accounts from home, all
dependent on how your mail server is configured:
1) It may be accessible by the POP3 or IMAP email protocols. IMAP
would be preferable since you can read the mail and leave a copy on
the server so it's still accessible at work. It is easy to set this up
in your email client, you just need the name of the server (or IP
address), and your username and password.
2) It may be configured to allow web access; just point your web
browser at the email server and log in with your username and account.
3) The above two are fairly standard and don't require that you log
into the actual work network just the server. Barring the above, you
may be able to use a VPN client to access the work network from home.
4) You may be able to use VNC to access your actual workstation at
work from your home PC.

These range in complexity and require information and possibly some
configuration changes from your network admin, so you should start
there.

http://www.uwsp.edu/it/exchange/offcampus.htm has some info about a
similar question.