I want to add a fully functional search engine to my website. What
software, or technology or service do I need to buy or lease to have a
search engine installed on my website (to search outside of my site as
well -- i.e., like GOOGLE?

Hi -
 
Looks like you need the Google Search Appliance.   "Install the Google
Search Appliance and you'll be impressed how much content it finds.
From product information to engineering documents and CRM knowledge
bases, the Google Search Appliance puts all the content on your
intranet and website one click away. "
 
Here's the home page on it:
  
Google Search Appliance
://www.google.com/appliance/index.html
  
Here's a feature listing:
://www.google.com/appliance/features.html
 
There's a frequently asked questions page on it as well:
://www.google.com/appliance/faq.html
 
 
If you need any additional information, please ask before rating this
answer.  Thank you for your understanding.
 
jbf777-ga
GA Researcher

i don't have experience with the google product and i'm sure it is
just fine. however you should review competing products before making
a commitment. i do have experience with "atomz search" from atomz.  it
can be found at http://www.atomz.com. the atomz search is a strong
application with an impressive user list also available for your
review on the atomz site. if you go to the site click on "atomz
search" near the top of the page between "atomz publish" and "atomz
promote". good luck in your search.

OR u could just use the Google code on ur website...
://www.google.com/services/free.html
unless of course u want to build ur own BRAND of search engine it is a
reasonable solution. it provides users to search ur website. and also
the internet .  :)