Measure the remaining concentration of reactant at various points in time. The graph that results will be a curve that goes downward but that slopes more and more gradually as time goes by, as the reactant will disappear less and less quickly as concentration drops.
Draw a line through any one of the points on your curve. Extend that line to at least one other point.
Use the two points to come up with the slope of the line that goes through them, using this formula for points (x1, y1) and (x2, y2):
(y2-y1)/(x2-x1) = m
where m is the slope of the line.
Change the sign in front of the answer to Step 3. You'll get a negative number, because slope on a downward line is negative. However, the rate of reaction measures consumption, so it should be positive. Once you've changed the sign, you have the instantaneous rate of reaction in moles per second.