This construction assumes you are already familiar with Constructing the Perpendicular Bisector of a Line Segment.

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.