Winding a bobbin is a simple act, but there are some things to know. You want to wind the weft tightly and uniformly. I begin by holding the bobbin in my dominant hand with the tip pointing toward me.
I take the weft yarn and hold it parallel to the shank with the cut end under my fingers. 
Next I wrap the weft over itself to lock it onto the bobbin. 
I am right handed, but if you are left handed you may want to do the opposite. 
I keep wrapping after pushing the weft close to the knob of the bobbin. Note that the weft goes over the top and hangs down the front. Watch the videos below to see the process in action. You want to wind the weft evenly across the bobbin shank. As soon as the weft comes near the height of the knob and shoulder of the lower half you want to shorten your passes of winding so you have a rounded bundle on your bobbin.
When done you can do a half hitch to lock the weft in place. I do this when I am done weaving with a bobbin and it can hang from the weaving without unwrapping like it does when I drop a bobbin.
In the videos below I am winding several strands together so I keep smoothing out the strands so they wind evenly.