This is what you need on your home computer:
1. A user account with a password
2. If you have a router: Forward port 3389 from your router to your computer*
3. Open port 3389 in your firewall

At work you don't have to do a thing, Remote Desktop Web Connection operates through port 80 as far as I know. At my workplace, all ports except port 80 are closed, and this works, so...

If it still doesn't work, please let me know the exact error messages you get.



*this is because your router has the external IP that you connect to, and your computer has an internal IP. Unless you forward the port, all traffic to your external IP/server name through port 3389 will never reach your computer.
There may be exceptions, check your internal IP (Start>Run> type: ipconfig to see IP Address), then check your external IP (http://checkip.dyndns.org/). If they are the same, no port forwarding is needed.