Gather data as you ordinarily would. For example, on January 1, 1900, the Dow Jones Industrial Average (DJIA) was about 50. On January 1, 1950, it was about 250, and on January 1, 2000, it was about 10,000. (You would plot many more points than this).
Choose endpoints for the axes. The endpoints should encompass the full range of data. In the example, the x-axis should cover 1900-2010, and the y-axis 10 to 15,000.
Choose tick marks. Depending on the size of the graph, 10 to 20 tick marks on each axis should be enough. These should divide the axis equally. In the example, the x axis could be every 5 years, so you would have ticks at 1900, 1905 and so on. On the y-axis, however, the tick marks have to be at multiples of each other. So, you could have tick marks at 50, 100, 200, 400, 800, 1600, 3200, 6400 and 12,800.
Plot the points, using the tick marks as guides.
Add a line connecting the points, if you wish.