How do I remote connect from my home pc (windows 7 pro) to office pc(Vista ultimate)?

You do this the same as for any other remote connectivity. This wiki entry is a good starting point (replace home by office). Further reading: the HowTo and the tutorial.
Come back to edit your question with any specific details you may stumble over to get this working.
Btw, the default port number to be used for remote desktop would be 3389.