Thanks my friends!
The information you gave me was very helpful. Now I have to -both- keep on reading and keep on trying :-)
The only thing that isn't too clear yet are the steps to install multilib in order to install both 32 and 64 bits applications. Yes, I know, I have to read http://connie.slackware.com/~alien/multilib/
but I am very tired now. I will try later :-)
I am very happy with the results: In a couple of days I've got my Slackware system up and running (Openoffice, VLC, Tvtime, etc, etc :-)