Suppose you have many frames, you have to create instance variables for that purpose.
If you don't know what an instance variable see this tutorial.
Lets see an example:
This will be your frame that sends the variables :
public class MainFrame {
    public void actionPerformed(ActionEvent ev) {
    String user = userField.getText();
    String pass = passField.getText();
    FrameOne frameOne = new FrameOne();
    frameOne.setUser(user);
    frameOne.setPass(pass);
    /* 
     * You've passed the user and pass to other frame,
     * now you can make it visible.
     */
    frameOne.setVisible(true);
 }
And this will be your first frame:
public class FrameOne extends JFrame {
    private JTextField userField;
    private JTextField passField;
    // then create setters and getter
    public void setUser(String user) {this.userField.setText(user);}
    public String getUser() {return this.userField.getText();}
    public void setPass(String pass) {this.passField.setText(pass);}
    public String getPass() {return this.passField.getText();}
    public FrameOne() {
        //define the components here
    }
}
NOTE : I didn't compile the code, this is only for demonstration on your problem.