Unlike 120 volt systems, the wire used in low voltage systems does not have to be buried deep or in conduit. Since there is no chance of getting shocked, the wire is left above ground in the flower beds but under the mulch. If you redo your beds or plant annual flowers you will see the wire when you pull back the mulch. This avoids cut wires.
The wire going across the grass is buried below the surface. There is no need for trenching.
You may not even notice any changes to your property other than the wonderful atmosphere created by your lighting system.