A hodograph is a visual depiction of the vertical distribution of wind throughout the atmosphere.
Hodographs are constructed on a polar coordinate plot, which enables you to map winds based on direction and speed with height from the origin or center of the plot. Once you plot winds at different levels of the atmosphere, lines are drawn to connect the dots to give the hodograph it’s shape.
Plotting a hodograph means working in the inverse. So a southwest wind will be plotted northwest of the point of origin and a north wind would be plotted to the south. On a hodograph, you plot where winds are blowing not where they are blowing from.
Determining shear vector is also relatively easy, as you simply draw a line from a point of origin to the corresponding dot. Generally, and practically, you are interested in the 0-6km shear vector for storm chasing. This is because parallel shear vectors to the initiating boundary tends to indicate the likelihood of storm lines vs. perpendicular vectors to the boundary which tend to indicate isolated storm modes.