It's definitely a good idea to blow the water out using a compressor. Since naturally there will be sections of the system where water will sit, and the pipes are not very deep (typically 1 or 2'), they will likely freeze, and if that happens the pipes will crack, and you'll have a non-working system (and lots of digging to do) in the spring.
Check this question for advice on how to connect a compressor to the sprinkler system. It's best to blow out each zone one by one, so that you don't end up with water stuck in one line still while all the air escapes out another already-empty zone. Start with the zone with the highest elevation, if possible, and go down from there. You may need to cycle back through one more time.
Once you have the fittings ready to connect your compressor to the system, it's a pretty quick job, should only takes a few minutes really. Once there is air coming out of the zone, you're good and can move on to the next.
50 PSI is about the max you'd need on the sprinkler system side. Be careful going higher - 100 PSI is probably higher than the pipes/fittings used for sprinklers (or the sprinklers themselves) can handle.
From the corrosion, I'm guessing this has been leaking for a while. If it's just a bad threaded joint, then you just need to unscrew the fittings, starting at the closest union, clean the threads, reapply some pipe dope to the male threads, and screw them back together in reverse order. It's a pretty easy repair requiring a couple of large wrenches, a wire brush, and pipe dope. If you have an inside shutoff to just this line, it's very DIY.
If the valve is leaking from the stem, and that's a 1/4 turn shutoff, then you should simply replace it. These tend to be very nice valves, but there isn't much to repair when they fail.
If a soldered joint is leaking, then the pipe should be cut and soldered again with new sections of pipe.
Unless this has been leaking ever since the installation, I'd guess it failed from freezing. Make sure these lines are fully drained in the winter, or wrap them with heat tape and insulation, to prevent freezing and damage in the future. And if you don't have an inside shutoff to this line, you really should get one added, along with and a drain line.
The valve is turned off because the pipe directly after the valve has come loose from the valve. I'd like to repair this, but I'm not sure what the grey/brown piece just below the valve is: 
Here are a few more shots of the side and the cap on the part that sticks down: 
Best Answer
That is a strainer wye. There is a metal mesh filter in there to trap sediment/debris; it can be removed and cleaned as necessary.