Clean out the area around the damage very well, so you don't end up with contaminated splices. That break looks like it's on a curve. If you can straighten-out that curve you may
be able to create enough extra wire so you don't have to splice-in a replacement piece, which would double your work.
Cut out the damaged bits. You don't necessarily
have to discard all
the exposed conductors where the individual insulation is still intact.
When splicing you have two or three options. For the electrical aspect you can either perform what are known as "Lineman" or "Western Union" splices or use double-ended barrel crimps. If you splice, soldering is optional. (If you don't know how to solder, best skip it entirely.)
Whether you splice or crimp, you want to use shrink tubing over each splice. If you use adhesive-lined heat shrink it will ensure both water-tightness and mechanical integrity. There are wire crimp connectors that come with integral adhesive-lined heat shrink tubing.
The downside to crimping is most people wouldn't know a proper crimp from a hole in the ground. This can be mitigated with proper
crimpers, but such crimpers are relatively expensive for a one-off repair job.
Then, once everything is spliced back together, self-vulcanizing tape (not
plastic/vinyl electrical tape!) around the whole thing. (You can also use very large diameter shrink tubing--either adhesive lined or taped with self-vulcanizing tape at each end.)
For all heat shrink tubing: The un-shrunken I.D. should be about double the O.D. of the wire or cable to which it will be applied. (You can go smaller if you know what you're doing. Don't go larger or it may not shrink down far enough.)
Advanced technique: To keep the bundle of splices from getting too fat, stagger the individual splices.
Underground wiring must be rated for wet locations even if the wires or cable are in a conduit.
It's low-voltage. Not really an issue in this case, except for longevity.