Call variable from other java class

Question 1

One problem I see is that your LoginScreen class is a JFrame, and a JFrame's behavior is to not stop program flow from the calling code when it is displayed, so even if you could extract the login name and password from this object in your later code, you'll be extracting it too early, before the user has had a time to enter anything.

Suggestions:

Most important is that you're trying to run code that won't compile. Never do this as this is guaranteed to always fail. Instead, fix compilation issues before trying to run your program.
Your LoginScreen should be a modal JDialog and not a JFrame.
You first display this window in order to get the user's input.
Key point here is, that because it is a modal JDialog, the calling code flow stops when the dialog is displayed.
The calling code then resumes once the dialog has been dealt with and is no longer visible, meaning once the user has either entered data or canceled the dialog.
At that time, you then get the login user's name and password (best if the latter is obtained as a char[]) from the LoginScreen instance by calling getter methods, and checking to be sure that they are not null. i.e., LoginScreen should have a public String getUserName() method and a public char[] getPassword() method.
The calling code can now use this information in the database.
And yeah, please learn Java naming conventions, and please comply with them by having your class names start with upper-case letters and method and variable names with lower-case letters. This will make it easier for folks trying to understand your code and help you, namely the volunteers here, do it better.

Edit

Note also that a JOptionPane is really nothing more than a modal JDialog, and this can be used for your purposes as well, and easily too. For example, in the example code below I create an InputForm JPanel and then place that JPanel into the JOptionPane:

import java.awt.GridBagConstraints;
import java.awt.GridBagLayout;
import java.awt.Insets;
import java.awt.event.ActionEvent;
import java.awt.event.KeyEvent;

import javax.swing.*;

@SuppressWarnings("serial")
public class MainFoo extends JPanel {
   private static final int COLUMNS = 10;
   private JTextField userNameField = new JTextField(COLUMNS);
   private JTextField passwordField = new JTextField(COLUMNS);
   private InputForm inputForm = new InputForm();

   public MainFoo() {
      add(new JLabel("User Name:"));
      add(userNameField);
      add(Box.createHorizontalStrut(15));
      add(new JLabel("Password:"));
      add(passwordField);
      add(new JButton(new LogInAction("Log in", KeyEvent.VK_L)));
   }

   private class LogInAction extends AbstractAction {
      public LogInAction(String name, int mnemonic) {
         super(name);
         putValue(MNEMONIC_KEY, mnemonic);
      }

      @Override
      public void actionPerformed(ActionEvent e) {
         int result = JOptionPane.showConfirmDialog(null, inputForm, "Input Form",
               JOptionPane.OK_CANCEL_OPTION, JOptionPane.PLAIN_MESSAGE);
         if (result == JOptionPane.OK_OPTION) {
            userNameField.setText(inputForm.getUserName());


            // ***** never do this! ***** 
            // Never change a password into a String.
            // This is for demo purposes only.
            passwordField.setText(new String(inputForm.getPassword())); 
         }
      }
   }

   private static void createAndShowGui() {
      JFrame frame = new JFrame("MainFoo");
      frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
      frame.getContentPane().add(new MainFoo());
      frame.pack();
      frame.setLocationRelativeTo(null);
      frame.setVisible(true);
   }

   public static void main(String[] args) {
      SwingUtilities.invokeLater(new Runnable() {
         public void run() {
            createAndShowGui();
         }
      });
   }
}


@SuppressWarnings("serial")
class InputForm extends JPanel {
   private static final int COLUMNS = 10;
   private static final int GAP = 3;
   private static final Insets LABEL_INSETS = new Insets(GAP, GAP, GAP, 15);
   private static final Insets TEXTFIELD_INSETS = new Insets(GAP, GAP, GAP, GAP);
   private JTextField userNameField = new JTextField(COLUMNS);
   private JPasswordField passwordField = new JPasswordField(COLUMNS);

   public InputForm() {
      setLayout(new GridBagLayout());
      addLabel("User Name:", 0);
      addTextField(userNameField, 0);

      addLabel("Password:", 1);
      addTextField(passwordField, 1);

   }

   public String getUserName() {
      return userNameField.getText();
   }

   public char[] getPassword() {
      return passwordField.getPassword();
   }


   private void addTextField(JTextField field, int row) {
      GridBagConstraints gbc = new GridBagConstraints();
      gbc.gridwidth = 1;
      gbc.gridheight = 1;
      gbc.gridx = 1;
      gbc.gridy = row;
      gbc.anchor = GridBagConstraints.EAST;
      gbc.fill = GridBagConstraints.HORIZONTAL;
      gbc.insets = TEXTFIELD_INSETS;
      gbc.weightx = 1.0;
      gbc.weighty = 1.0;
      add(field, gbc);
   }

   private void addLabel(String text, int row) {
      GridBagConstraints gbc = new GridBagConstraints();
      gbc.gridwidth = 1;
      gbc.gridheight = 1;
      gbc.gridx = 0;
      gbc.gridy = row;
      gbc.anchor = GridBagConstraints.WEST;
      gbc.fill = GridBagConstraints.BOTH;
      gbc.insets = LABEL_INSETS;
      gbc.weightx = 1.0;
      gbc.weighty = 1.0;
      add(new JLabel(text), gbc);
   }
}

Question 2

Is it really your goal to have the loginscreen be global to all instances of your cagbas classes? I'm guessing you want to define loginscreen logindetails as class variables but you want to instantiate them during cagbas class creation/initialization.

Something like this:

public class cagbas extends javax.swing.JFrame {
    loginscreen logindetails;
    String uname;
    String pass;
    ....
    public cagbas () {
       initComponents();
       logindetails = new loginscreen ();
       uname = logindetails.getUsername();
       pass = logindetails.getPassword();

One style note, capitalize your classnames.

[edit]
You can't access uname in main because main is static and uname is not. Move that assignation into a function AFTER you instantiate your Cagbas class.
[/edit]