There is I'm told asbestos in my basement floor and also on the duct
work in the basement.  Is this serious, and if so, how? and how do I
solve it?

Perhaps this will be helpful to you.

http://www.hometips.com/articles/asbestos4.html

http://www.findarticles.com/p/articles/mi_m1216/is_n3_v181/ai_6607022

The first thing I would do is get a sample(s) and send it to a lab for testing.
http://www.asbestostestinglab.com/index.html 
The price varies by turn around $65 for 5 Days to $110 for 24 Hrs to
$250 for 1 Hour.

Years ago, I had a professional come out to my home to evaluate what
the best solution would be for us.  About half of our ductwork in the
basement is covered in asbestos.  He came to the conclusion that it
would probably be more economical to leave it be rather than to remove
it.  Our basement isn't used for much more than laundry, and as long
as it isn't disturbed, the asbestos should pose no threat.

As to the asbestos in the flooring, I can't speak personally to that. 
The links below should be of help to you:

http://www.asbestos-institute.ca/home/home_ala.html

http://www.cpsc.gov/cpscpub/pubs/453.html

http://www.epa.gov/asbestos/pubs/ashome.html