the lolly pop end on the brake cable should be about the size of the round hole in your handle. Looks like you may have a bicycle shifter cable
You put it in from the top so the lolly pop fits in the hole, and the cable slides in the slot facing forwards, then rotate the cable toward the center of the bike (so the cable slides in the slot in the front of the handle (doesn't look like you've got an adjusting screw on that type handle, it may be on the brake)
Then run the cable housing over the cable, and route it to your brake, run the cable thru the adjuster/housing stop, and thru the clamp bolt. Adjust, tighten the clamp bolt and your done.
I usually lube the cable housing prior to putting it on the cable