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How do I draw something in a JPanel after I already called the paintComponent method

I'm new to making GUIs in Java. As I understand, there's a class called Graphics which is in charge of drawing shapes in a JPanel. When my application starts, I call the paintComponent method, which draws the board of the game I'm programming, and the paintComponent method takes a Graphics g as input. However, later on, I want to update the board, so how do I tell the same g that drew the board at the start of the game to draw something else when the user does something like clicking?
I believe this should have a very simple answer.

Every JComponent (Swing component) has a repaint() method, just call it to tell the DrawingManager to redraw your component.
All your drawing code should be in paintComponent method, that means that you don't draw anything anywhere else (you draw only in the flow of invocation of paintComponent, you can have drawing code structured in methods of course).
This method needs to have access to the state that indicates what and where should be drawn. It is because the OS could request repainting, and then only the painting methods from JComponent are called.
When you invoke repaint() on your JComponent, then in short time the paintComponent() method of the component on which you requested repainting will be called by the drawing thread, and you should draw only in this drawing thread.

Try repaint() or revalidate(), it should work.

I call the paintComponent method
No, you should never call the paintComponent() method directly. Swing will call the method for you when the component needs to be repainted.
I want to update the board
Then you need a "setter" method. Think of other Swing components. They have methods like "setForeground(), setBackground(), setText()" etc.
So if you want to change your component then you need to create appropriate setter method to change the properties of your class. Then in the method you save the property and simply invoke repaint() and Swing will repaint your component. So now your paintComponent() method needs to check the property you just set to do the appropriate painting.
public void setSomeProperty(Obect someProperty)
{
this.someProperty = someProperty;
repaint();
}
....
protected void paintComponent(Graphics g)
{
super.paintComponent();
// paint the board
if (someProperty != null)
// paint the property
}

Drawing a graph with Graphics2D using WindowBuilder

So I have a JPanel called displayPane and I want to make it a drawing area for a graph (I am making a graphing calculator). I am using WindowBuilder and this is the generated code for the JPanel:
JPanel displayPane = new JPanel();
displayPane.setBackground(Color.WHITE);
displayPane.setBounds(173, 33, 455, 432);
frame.getContentPane().add(displayPane);
After that I want to draw the axis of the graph but I have no idea how.
I've searched everywhere about it but everyone constructs a member class or something in the main class and adds the paintComponent(Graphics g) but that confuses me. What is that trying to accomplish ? Or just give me your way of doing it I don't really care as long as I understand it.
Any help is appreciated :)

Since this is homework, I'm going to give you general guidance without code, but first and foremost, please read this link on performing custom painting with Swing. Next you should put the Window Builder software to the side and work on creating your own code from scratch, at least do this til you're comfortable coding with Swing.
Next suggestions:
Have your DrawingPanel extend JPanel
Override paintComponent(Graphics g)
Call the super's method in your override, super.paintComponent(g) as this will refresh the graphics and erase old "dirty" pixels.
Play with drawing lines using g.drawLine(...)`
keep doing this and you'll get the idea of what you'll need.

Custom painting is achieved by overriding the paintComponent method of a JComponent based class (like JPanel).
This gives you access to the drawing surface onto which content is drawing and eventually shown on screen
See Custom painting and Painting in AWT and Swing for more details.
The Graphics API (or more specifically, the Graphics2D API) is a power abstract toolkit which provides with the means to actually paint stuff to the screen.
At the basic level, this provides you with the ability to specify colors and draw basic shapes and text. At a more complex level, you can define you own shapes, perform more complex coloring effects, including gradient fills and transformations of the basic context
See the 2D Graphics Trail for more details.

Double buffered image example in Jpanel

I would know if my implementation is correct for double buffered image.. because i note that tremble the borders of my image that i move in the screen ... It is normal??
public void paintComponent(Graphics g) {
Image bufferimage= createImage(180,180);
Graphics dbg= bufferimage.getGraphics();
//clean the screen
dbg.setColor(new Color(100,100,100));
dbg.fillRect(0,0,getWidth(),getHeight());
if (game_is_running) {
// draw various type of object with drawImage
for(int i=0; list[i]!=null; i++) {
list[i].draw(dbg);
}
target.draw(dbg);
I.draw(dbg);
}
//finally draw the image linked to graphics
g.drawImage(bufferimage,0,0,this);
}

Move the creation of the bufferimage out of the paintComponent() method. You don't need to create this every time that method is called. You are drawing the whole surface anyway.
When you are done with the Graphics retrieved from bufferImage (i.e. dbg variable in your case) you are supposed to call dispose() on it.
Finally you might be able to get away without the second image if you ensure that your component and the components that contain it, have the property doubleBufferred set to true.

All the paintComponent() method should do is draw the image.
The "if game is running" code does not belong in the paintComponent() method. The idea is to have a Timer or something that changes the state of your game and does the custom drawing on your image. Then when Swing invokes the paintComponent() method you simple paint the image in its current state.
Take a look at the DrawOnImage example from Custom Painting Approaches. The code adds rectangles to the image by using the mouse. Then whenever the component is repainted the image is painted.
The ideas is to create/modify the image once and then repaint the image. In a game it may turn out that every time you modify the image you also paint it, but the code should not be part of the paintComponent() method.

panel with image background and mouse draw

How can I use a image as background in a JPanel if the paint () method is already used for other purposes? (I'm tried to draw over a image in a panel).
Here is my code to draw as a pencil, but I don´t know how to add the image as background ?
#Override
public void paint(Graphics g) {
if (x >= 0 && y >= 0) {
g.setColor(Color.BLACK);
g.fillRect(x, y, 4, 4);
}
}
Thanks Diego

Suggestions:
Don't draw in the JPanel's paint(...) method but rather use it's paintComponent(...) method. There are several reasons for this, one being that if you use the paint(...) method, then you are also responsible for drawing the JPanel's borders and child components and at risk of messing up the rendering of these guys. Also you lose Swing's automatic double buffering.
First call the parent class's super method before calling any other code in the method. This will allow the JPanel to refresh its background and do any graphics housekeeping that may need to be done.
Next draw your background image using g.drawImage(...),
Then do your pencil drawing.

Hovercraft Full Of Eels gave good advice on one direction to take. Here is another.
Display the image in a (ImageIcon in a) JLabel.
When it comes time to paint:
Call createGraphics() on the BufferedImage to gain a Graphics2D object.
paint the lines or other visual elements to the graphics instance.
dispose of the graphics instance.
Call repaint() on the label.
E.G. as seen in this answer.

creating a pen tool, repainting issue - JAVA

I am trying to create a pen tool using mouse listeners:
public void mouseDragged(MouseEvent e) {
imageL.setCoordinates(originalPos, e.getPoint());
imageL.repaint();
originalPos = e.getPoint();
}
The paint function in the JLabel (imageL) receives two sets of points that allow drawing a line based upon the mouse drag. The only issue is that every time the drag is performed, the new layer does not contain the line drawn from the previous mouse drag. The paint function of the JLabel is as follows:
public void paint(Graphics g) {
super.paint(g);
Graphics2D g2d = (Graphics2D)g;
g2d.setRenderingHint(RenderingHints.KEY_ANTIALIASING,
RenderingHints.VALUE_ANTIALIAS_ON);
g2d.setColor(drawingColour);
g2d.drawLine(originCors.x,originCors.y,endCors.x,endCors.y);
}
So essentially my question is: How do I "add" the new line to the current layer?
any help would be great,
Thanks in advance

You want to draw in a JComponent's (and JLabel extends from JComponent) paintComponent method, not the paint method unless you plan to handle all the painting of the component's borders and children. Next, you may wish to have your drawing component hold an ArrayList of Point and add Points to this array list in the mouseDragged method. Then the paintComponent method can iterate through the list and paint all the lines. If all you want to do is paint one line, then have the painting JLabel hold both points in a class field.

Michael,
For a start, in swing (a JLabel is a swing component, as apposed to the older AWT library) the recommended practice is to override the paintComponent method (not the "paint" method). See The Java Tutorials: Custom Painting for the hows & whys of it.
If you want to custom-paint a-list-of-lines then you're going to have to do just that... not just the "new" one. One way around this is to "update" an image with each new line, and then custom-paint that... this is slightly quicker as you only "paint" the each line once, at the cost of using more memory (to maintain the "backgroun image")... but this technique lends itself to "double buffering", which avoids "that flickering" you get when you draw directly to the screen. See The Java Tutorials: Working with Images for the details. It's actually pretty straight forward.
I suggest you google for "java double buffering example" (avoid Rose India, it's full of crap).
Cheers. Keith.