Draw a cross on your graph paper. The horizontal line is the "x" axis, and the vertical line is the "y" axis. Mark 10 evenly spaced notches along the x and y axes. Starting from the center point, which always has a value of zero, label each notch from one to 10. The vertical axis has positive values on the top and negative values on the bottom. The horizontal axis has positive values to the right and negative values to the left.
Simple graphing starts with two numbers that are displayed like this: (x,y). If you had a point that was (1,1), count one notch to the right on the x axis and 1 notch up on the y axis. Mark that point with your pencil. Now mark points for (2,2), (3,3), (4,4) and so on through (10,10). You have now plotted 10 points in the top, right quadrant of your graph.
Connect each of the dots in order. Because both the x and y numbers are positive, increasing values, the line will go upwards from left to right. Also, since the increase in values here is continuous -- in this case advancing one point up and over each time -- the line from (1,1) to (10,10) is a straight diagonal.
Now plot a different set of values: (1,1), (1,2), (1,3), (2,3), (2,4), (2,5), (2,6), (3,6), (3,7), (3,8), (3,9). Connect them with a line between each point. This should create an upward zigzag line in the top, right quadrant of your graph.
Experiment with negative values. Start with a negative number for the x value and positive number for the y value. Values of (-1,1) continuously through (-10,10) would be a diagonal line upward in the top left quadrant. Similarly, values of (-1,-1) and so on would appear in the lower left quadrant; values of (1,-1) and so on would be in the lower right quadrant.
Sometimes you have to graph an equation, such as 2x+y=10. When you have an equation, plug in a series of x values to come up with a corresponding y value. For instance, if you put in a 0 for x, you would write 2(0)+y=10. The y in this case is 10. This makes your numbered pair (0,10). If you plugged in 1 for x, you would get 8 for y -- written as (1,8). Continue plugging in x values, derive the numbered pairs, plot them, connect them, and you will have a line graph that represents the equation.
With more advanced graphing you will be able to draw curved lines, parabolas (horseshoe shaped graphs) and other equations. Such advanced graphing is necessary in the field of computer animation, for instance. Basic line graphs, though, just involve plotting points and connecting them all together.