Turning off the Sprinkler system
So consumer level sprinkler systems are pretty simple things. In your case, you'll have 1: a pump near the well to generate enough pressure within your system, 2: a timing unit that acts as the brains/clock (usually at 24V), applying a voltage to likely your pump, as well as 3: those solenoids (those cylinders at the top which actuate) and 4: the actual hardware used in the irrigation system itself.  

As Tyson mentioned, most consumer setups that run off municipal water have enough head pressure to provide more than enough flow sufficient for a few acres. That pressure is there when you're tapping from your mains, so normally whoever plumbs it the new run will have a compression fitting in-line with the new piping throwing a 3/8" compression shut-off valve in-line. 

If you're sourcing from a well, you don't have that sorta constant pressure (or presumably any pressure at all until your motor kicks on, unless your lands water table is real wonky and your irrigation is significantly lower than where you hit water) to deal with so odds are they said screw it and didn't pay the $15 to couple one in. 

This is good news ! Assuming you're 100% sure you're getting well-water, You can likely work on that system without turning off any sort of mains off other than a pump. Ingress and egress (I'm not sure if those are the right flow terms, I'm in semiconductors professionally..) should have no back-pressure. 

I can't tell by that picture where the leak is, but check all of your seals first. I'd a boatload of money if you're leaking out where the solenoid actuator is coupled to the lower assembly on the T, it's just a bad ring. They're just like bearings (all standardized in sizes/ratings/etc) so you can swap them out yourself without having to call in some schmo and have him say you have to replace the whole unit because he doesn't want to waste his time to take it apart. You'll end up paying for a whole new unit plus his labor, rather than paying $12 for a seal from those over-priced vendors like McMaster and MSC (and really, unlike bearings which have build quality variance to them - a Buna-N seal is a Buna-N seal). If you have the datasheet from the vendor, it'll tell you the sizing, materials, etc. 

I'm not an electrician, it looks like that utility shaft isn't properly sealed so it's getting hit by some elements. It might be a huge pain depending on where you're sourcing your power from, but I'd definitely re-run that with exterior grade shielding, enclosed properly in a weather-resistant box. (Or completely eliminate the mains, buy an exterior enclosure and throw 8 AA's in there if 12v is the solenoid actuating level.)



Edit: To shut off that whole system, cut the three supply lines and PVC cement end-caps to them. I can't tell from the picture 100% if the flex-PVC or the hard schedule 40 is the source, but it looks like the sch.40 are all parallel so I'm guessing those are connected to a manifold which connects to the well/pump. Measure the size (just take a string and wrap it around, divide by 3.14 to get the "OD" (outer diameter). The sizings for PVC are in 1/4 inch so you don't need precision calipers to get a measurement. 

Find 4 fittings of that size at your local Home Depot. Buy that, some PVC cement, a hack-saw if you need it, and some 400-ish grit sand paper to clean up the ends of all that dirt so your adhesive bonds properly. (Those are just suggestions - use what you got. RE: Adhesive. If you have some 3M DP100 or JB Weld, those will work too, I'd bet. RE: Sandpaper. 400 grit isn't necessary, if you have a wire-wheel on your angle grinder/drill/whatever you can use that, or even a dremel with a deburring tool. RE: hacksaw - PVC is soft, any cutting tool will work.) Once the ends are clear of dirt, apply adhesive, cap them off with the new fittings. Working time is in the tens of minutes, cure time is usually 24 hours for adhesives of that form.

Electrically, those motors will continue to actuate. It will be a negligible amount of power and leaving them in line won't burn your house down. If you don't know how to decommission them - I'd leave them be, because if other appliances are on the same circuit and powered in series with your sprinkler assembly, they'll stop working. The "right" way to do it would be to find the junction box/circuit/sub-circuit box that it's sourcing from and to disconnect the wiring in a proper-up-to-code-NEC way, or to call a licensed electrician.