Keeping a permanent broadband connection

How can I keep my broadband connection permanently connected (when PC turned
on).
When I call upon Internet Explorer it tells me 'connecting' and after some
time I get access, however when I come out of IE it disconnects. If I wish
to go back into the internet I have to wait for it to reconnect again.
This seems to be relevant to an earlier posting of mine where I have said I
am unable to activate a weblink from an incoming e mail.
Suggestions are much appreciated.

John King