As Christopher says, learn loads of Slash songs/licks. Then you will discover in what kind of way he plays, it's rather difficult putting it up here in text.
Perhaps you can request a Slash Artist study here at GT, that should be awesome and I think LOADS of people will like that :-). Currently there are only three lessons I'm aware off in the style of Slash:
http://www.guitartricks.com/lesson.php?input=13649
http://www.guitartricks.com/lesson.php?input=13694
http://www.guitartricks.com/lesson.php?input=12689
Give these a try.
JJ