[python] How to embed matplotlib in pyqt - for Dummies

I am currently trying to embed a graph I want to plot in a pyqt4 user interface I designed. As I am almost completely new to programming - I do not get how people did the embedding in the examples I found - this one (at the bottom) and that one.

It would be awesome if anybody could post a step-by-step explanation or at least a very small, very simple code only creating e.g. a graph and a button in one pyqt4 GUI.

For those looking for a dynamic solution to embed Matplotlib in PyQt5 (even plot data using drag and drop). In PyQt5 you need to use super on the main window class to accept the drops. The dropevent function can be used to get the filename and rest is simple:

def dropEvent(self,e):
        """
        This function will enable the drop file directly on to the 
        main window. The file location will be stored in the self.filename
        """
        if e.mimeData().hasUrls:
            e.setDropAction(QtCore.Qt.CopyAction)
            e.accept()
            for url in e.mimeData().urls():
                if op_sys == 'Darwin':
                    fname = str(NSURL.URLWithString_(str(url.toString())).filePathURL().path())
                else:
                    fname = str(url.toLocalFile())
            self.filename = fname
            print("GOT ADDRESS:",self.filename)
            self.readData()
        else:
            e.ignore() # just like above functions  

For starters the reference complete code gives this output:

Below is an adaptation of previous code for using under PyQt5 and Matplotlib 2.0. There are a number of small changes: structure of PyQt submodules, other submodule from matplotlib, deprecated method has been replaced...

import sys
from PyQt5.QtWidgets import QDialog, QApplication, QPushButton, QVBoxLayout

from matplotlib.backends.backend_qt5agg import FigureCanvasQTAgg as FigureCanvas
from matplotlib.backends.backend_qt5agg import NavigationToolbar2QT as NavigationToolbar
import matplotlib.pyplot as plt

import random

class Window(QDialog):
    def __init__(self, parent=None):
        super(Window, self).__init__(parent)

        # a figure instance to plot on
        self.figure = plt.figure()

        # this is the Canvas Widget that displays the `figure`
        # it takes the `figure` instance as a parameter to __init__
        self.canvas = FigureCanvas(self.figure)

        # this is the Navigation widget
        # it takes the Canvas widget and a parent
        self.toolbar = NavigationToolbar(self.canvas, self)

        # Just some button connected to `plot` method
        self.button = QPushButton('Plot')
        self.button.clicked.connect(self.plot)

        # set the layout
        layout = QVBoxLayout()
        layout.addWidget(self.toolbar)
        layout.addWidget(self.canvas)
        layout.addWidget(self.button)
        self.setLayout(layout)

    def plot(self):
        ''' plot some random stuff '''
        # random data
        data = [random.random() for i in range(10)]

        # instead of ax.hold(False)
        self.figure.clear()

        # create an axis
        ax = self.figure.add_subplot(111)

        # discards the old graph
        # ax.hold(False) # deprecated, see above

        # plot data
        ax.plot(data, '*-')

        # refresh canvas
        self.canvas.draw()

if __name__ == '__main__':
    app = QApplication(sys.argv)

    main = Window()
    main.show()

    sys.exit(app.exec_())