1.
How do you set up a web site.
More of that later
2.
What is a web master.
The webmaster is typically the person who controls the site. In other words, if you were to set up a site you would be it's webmaster.
3.
What are the problems...spam etc.
This depends on a number of issues, mainly the solution you use to create the website. But things such as spam shouldn't be too problematic
4.
What does it cost.
How much do you want to spend? You can do it for nothing if you want, you can spend £100 or £10,000.
I think the real issue is you deciding what you want the site to do. Is it, in effect, a 'book on the web' which will simply display text and pictures?
The free solutions are either a blog or a wiki
BlogThis is more of a 'news' style approach to the web. I use a blog for my inane updates about my websites. They are very easy to use and tend not to be static an example is
http://westmeadanaesthesia.blogspot.com/! You decide to write something, post it, and that goes at the top of the page, pushing other articles below.
WikiThis has been made famous by wikipedia, but a clinical one is
http://www.ganfyd.org/index.php?title=Main_Page. These tend to be easy to use and are more like a book. You have a home page and you then link to other pages, which you create (very easily), add pictures etc.
As for writing websites from scratch using a bought programme, I would not be able to advise, I've not done that in 8-10 years.
But the main advice is to be very clear what you want to do and how the site might be structured. I'm more than happy to exchange e-mails with you regarding potential choices. If you go with a blog or a wiki I'm more than happy giving you a driving lesson on setting it up.