This is the stepbystep, printable version. If you PRINT this page, any ads will not be printed.
See also the animated version.
After doing this  Your work should look like this 

We start with a triangle PQR.  
First, we draw the median of the triangle through R  
1. Construct the bisector of the line segment PQ. Label the midpoint of the line S.
See Constructing a perpendicular bisector of a line segment 

2. Draw the median from the midpoint S to the opposite vertex R  
Next, we draw the second median of the triangle through P  
3. In the same manner, construct T, the midpoint of the line segment QR. See Constructing a perpendicular bisector of a line segment  
4. Draw the median from the midpoint T to the opposite vertex P  
(Optional step) Repeat for the third side. This will convince you that the three medians do in fact intersect at a single point. But two are enough to find that point.  
5. Done. The point C where the two medians intersect is the centroid of the triangle PQR. 