There are quite a number of companies offering a free search facility for exactly the reason that you identify, namely that
there is a demand for site searches but people don't really want to do it from the ground-up.
These usually work by building an index to your site in their own database, which is then updated regularly.
I am not sure whether these services can be tailored to query a database - probably not, in which case you would need to create
text files (HTML pages) and point the Search engine at those pages.
Right now,you have two possibilities :-
1) Choose one of these services,
2) Wait a week until I have finished building my own search facility.
Option 1) Commercial services :-
1.1) I have used a neat facility from Atomz, (www.atomz.com). 
     You can see it in action on one of my other Sites at :-
        http://www.kpisystems.com/site_map.htm
     If you type KPI in the 'general search' box, the search will return with 92 hits. 
     The layout is good and you can tailor it to match the house-style of your own Web Site.
1.2 A very impressive Site is http://www.thunderstone.com/ which offers a range of 'intelligent information-handling services'. Their Search
    services, called Webinator, are described on 
       http://www.thunderstone.com/jump/Search.html,
    where it says :-
      "Note: You can get a copy of this search software for your site,
       and if that's too hard we'll even maintain the site index for you!"
    You can see this is in use at http://www.rubus.com if you click on 'search'
1.3 I am currently developing a database-supported facility and with a natural language query for the DatabaseAnswers FAQs. The database is at :-
       http://www.databaseanswers.com/data_models/search_engine.htm
    The database is very simple and I'm doing it myself using MySQL to see if it really is as simple as it looks and because I can tailor it to suit myself.