The period of any function can be determine from the graph by determining the distance on the x axis (probably time in your case) it takes for the graph to complete one full cycle. A cycle is defined as the time it takes for the graph to start repeating itself. If you are dealing with a sine or cosine function this would be the distance between two peaks or two troughs (high and low points). If you are measuring the period starting at the mid point, the period ends when the function crosses the midpoint for the second time.
It is atypical that a graph would contain less than one period. However, if you are given one like this, try to identify the distance on the x-axis that it takes to make a half of the period. This amount can be doubled to determine the period. You can identify this on a trig function as the distance between a peak and trough or the distance between two midpoints.