Mark the location, size and outline of the desired trench. Apply spray paint directly to the concrete of the basement floor.
Break up the concrete floor with an electric jackhammer. Begin at the edge of the hole with the point bit of the jackhammer, making a crack to mark the outline of the proposed trench. Enlarge the outline cracks using the chisel bit, moving toward the interior of the marked area.
Remove pieces of concrete as they break off. Put them in a bucket or a wheelbarrow for removal and disposal.
Dig the trench using a small square spade. Use a garden trowel to dig out trenches narrower than about 6 inches. Place the dug-out dirt into a bucket or wheelbarrow to be removed.