The two easiest are via layering and/or cuttings.

Link for cuttings:

http://dspace.dial.pipex.com/clematis/prop.htm

Link for layering:

http://www.rhs.org.uk/advice/profiles0602/layering.asp

Starting from seed can also be done but any plants from seeds of hybrids may or may not look anything like the parent plant. See the thread titled toki propagation for a link on how to start clematis from seed. Be prepared for a long wait depending on the type of seed you start as some may take a year or longer to germinate.