Alternatively, could you not make an instance of AllStudent before invoking the add() method? e.g.
public class AllStudent {
LinkedList students =new LinkedList();
public void addNewStudents(Student s){
students.add(s);
} //end addNewStudent
public static void main(String[] args) {
AllStudent example = new AllStudent(); //create a new AllStudent object called 'example'
example.addNewStudent("fgk"); //use example's addNewStudent method to add a new student 'fgk'.
} //end main
} //end class
Then, you're creating an instance of the class from Main, and using that instance to access the nonstatic content as opposed to making everything static. addNewStudent(Student) invoked the add() method for the linked list anyways, so you can create the class instance from Main(String[]), and then use the addNewStudent method to add a new student instead of trying to add it directly.
I'll ask a lot of questions (most of them probably stupid stuff). Bear with me, i'm still learning! ^_^ Also, I'll try to answer as many questions as I can as well, but I'm not very good yet. I'm sure I'll be of more use once I get better :)