How to add a JButton into the center of a JFrame with BorderLayout()? I tried using BorderLayout.CENTER, but instead of the center
It may take some time to learn, but SpringLayout is worth looking into. It will let you position elements on the GUI where you wish. You can look here for examples of different layouts.
Put a JPanel in the CENTER and set the layout to GridBagLayout or BoxLayout as seen in this answer to Set component at center of the page.

The GridBagLayout is used to center a label containing the yellow/red gradient image seen in the Nested Layout Example.

try this
frame.getContentPane().setLayout(new BorderLayout(0, 0));
JButton btnNewButton = new JButton("New button");
frame.getContentPane().add(btnNewButton, BorderLayout.CENTER);