Q: Cannot make a static reference to the non-static method Library my professor refuses to tell me what I'm doing wrong and I for the life of my can't figure it out. I'm just starting java so I may look foolish but
import java.util.Scanner;

public class Library {
    MediaItem[] items = new MediaItem[100];
    int numberOfItems = 0;
    static int displayMenu(){
        @SuppressWarnings("resource")
        Scanner dog = new Scanner(System.in);
        System.out.println("Menu:\n1:Add New Item\n2:Mark Item as Loaned\n3:List All Items\n4:Mark Item as Returned\n5:Quit");
    int cat = dog.nextInt();
    return cat;
}
void addNewItem(String title, String format){
    MediaItem item = new MediaItem();
    item.setTitle(title);
    item.setFormat(format);
    items[numberOfItems] = item;
    numberOfItems++;
}
void markItemOnLoan(String title, String name, String date){
    for (int i=0;i<numberOfItems;i++){
        MediaItem item = items[i];
        String title5 = item.getTitle();
        if (title5 == title){
            item.markOnLoan(name, date);
            i=numberOfItems;
        }

        }
}
String[] listAllItems(){
    String[] all = new String[numberOfItems];
    for (int i=0;i<numberOfItems;i++){
        MediaItem item = items[i];
        if (item.onLoan=true){
            all[i]=item.getTitle()+" "+item.getFormat()+" "+item.getOnLoan()+" "+item.getLoanedTo()+" "+item.getDateLoaned()+" ";
        }else{
            all[i]=item.getTitle()+" "+item.getFormat()+" "+item.getOnLoan()+" ";
        }

    }
    return all;
}
void markItemReturned(String title){
    for (int i=0;i<numberOfItems;i++){
        MediaItem item = items[i];
        String title1 = item.getTitle();
        if (i==numberOfItems){
            System.out.println("Title not found.");
        }else if (title1 == title){
            item.markReturned();
            i=numberOfItems;
        }
        }
}

public static void main(String[] args) {
    Library banana = new Library();
    String invalid = "Invalid Option";
    @SuppressWarnings("resource")
    Scanner dog = new Scanner(System.in);
    for (int i=0; i==0;){
        int cat = displayMenu();
        if (cat<=0){
            System.out.println(invalid);
        }
        if (cat>=6){
            System.out.println(invalid);
        }
        switch (cat){
        case 1:
            System.out.println("What is the title of the item?");
            String title = dog.nextLine();
            System.out.println("What is the format of the item?");
            String format = dog.nextLine();
            banana.addNewItem(title, format);
            break;
        case 2:
            System.out.println("What is the title of the item?");
            String title1 = dog.nextLine();
            System.out.println("What is your name?");
            String name = dog.nextLine();
            System.out.println("What is the date?");
            String date = dog.nextLine();
            banana.markItemOnLoan(title1, name, date);
            break;
        case 3:
            String[] list = banana.listAllItems();
            System.out.println("List of all items:\n");
            for (int o=0;o<banana.numberOfItems;o++){
                System.out.println(list[o]);
            }
            break;
        case 4:
            System.out.println("What is the title you are returning?");
            String title2 = dog.nextLine();
            banana.markItemReturned(title2);
            break;
        case 5:
            i++;
            break;
        }
    }
}
}

I'm having this problem throughout my code but I figure if you guys can answer this one I can figure the rest out on my own.
Edit: I'm getting further, now I just need to figure out why it isn't reading the name and date.

A: In your switch statement, you call addNewItem, which is not declared static. 
In order to call addNewItem, you must have an Object to call it from, unless you declare it static, or call obj.addNewItem(). You didn't include much code, so I'm not sure what class the object should be. 
static void addNewItem(String title, String format){
    MediaItem item = new MediaItem();
    item.setTitle(title);
    item.setFormat(format);
    items[numberOfItems] = item;
    numberOfItems++;
}

the static keyword means that there is only a single instance of the method, field, or class even if there isn't an instance of the class associated with it. Without the static modifier, there needs to be an instance of the class to access the method, field, or class from. 
For a good example, see: https://stackoverflow.com/a/15828090/1732480
Edit: After you posted more code, you have no instance of Library to call addNewItem on. 
Create a Library with Library l = new Library(); and call l.addNewItem()
public static void main(String[] args) {
    Library l = new Library();
    String invalid = "Invalid Option";
    Scanner dog = new Scanner(System.in);
    for (int i=0; i==0;){
        int cat = displayMenu();
        if (cat<=0){
            System.out.println(invalid);
        }
        if (cat>=6){
            System.out.println(invalid);
        }
        switch (cat){
            case 1:
                System.out.println("What is the title of the item?");
                String title = dog.nextLine();
                System.out.println("What is the format of the item?");
                String format = dog.nextLine();
                l.addNewItem(title, format);
                break;
         ....

