Many people own an edger or have a neighbor that will lend them an edger making this method cheaper than renting a trencher. It does however take a bit longer since you need to bury the cable by hand, unlike a trencher which will dig the hole and bury the cable in one step. You can use either an electric or gas powered edger, the later tend to be more powerful and are preferable.
Set the power edger to the deepest setting and use the edger to dig a trench along the desired wire path. Go nice and slow and when turning, start the turn early and remember to make gradual arcs to avoid creating right angles. If the ground is hard, you may want to do this in two passes, a first pass at a shallow depth and a second pass with the edger set to the deepest setting.
It can sometimes help to moisten the ground a little an hour before cutting your trench. Wet ground will not kick up as much dust and will help the trench retain it’s wall integrity. But, beware too much water will create a mud bath.
Next, place the wire in the trench you created. You can poke the wire into place with a screwdriver, stick, or one of the boundary flags. You want that wire to be as close to the bottom of the trench and possible to avoid the wire floating to the surface. If the wire does not want to stay in place, you can try using some lawn staples to hold the wire down at the bottom of the trench. Now bury the wire with the dirt that was displaced by the edger. Finally, stomp on the dirt to compact it into place. If the dirt is too scattered to kick or rake back into, just get a bag of garden soil from your local hardware store or nursery and use that to back-fill.