If you follow the example in the manual, for any user who has disabled cookies the constant SID will be set to the value of the session ID and can be inserted in URLs as the first token, before any other arguments. For any user who has enabled cookies, SID will be unset.
I have not bothered to worry about users who disable cookies, figuring that most of them are conspiracy theorists who will only make nuisances of themselves if allowed onto a BBS. :-)
As for session_register(), you call it with the name of each variable that you wish to store persistently on the server:
$foo = "this is a string";
$bar = "5";
session_register("foo");
session_register("bar");
Now, on subsequent pages you can do this:
session_start(); // restore variables
echo "foo is $foo, bar is $bar";
