You certainly can make a 'professional' web site using free tools - in fact,
many if not most professional web site designers will be crafting html and
css code using simple text editors, which could be Notepad or Wordpad on
windows, but better programs include Textpad and Notepad++ , which are
cheapish and free, respectively.
You will need an image editor of some sort in addition - professionals will
probably use Adobe Photoshop but Paint.Net is free.
It's essential to learn HTML & CSS - plenty of free resources are available
to help with this - one of the best at
www.w3schools.com
Unfortunately if you need any animated or dynamic graphics then you may need
to purchase a commercial program for best results - Adobe Flash is probably
the commonest solution at the moment, but Microsoft Silverlight is upcoming.
Don't even dream of using Publisher though - it's simply incapable of
producing a 'professional' standard web site and in it's forthcoming 2010
guise can't produce any sort of web site at all as the facility is being
removed.
Professionals, on the windows platform, are likely to be using Adobe
Dreamweaver or Microsoft Expression Web. Both of these are available in free
trial versions, but the former is not cheap.