Oh, I like this thread, so I'll take a crack at it.
Unfortunately I will probably not work with an instructor this year due to no one in my current area, but I have the last couple seasons.
I'd usually go once a week. The big thing was doing work on my own, I know way to many kids that the only time they touch their gear in the offseason is for their lesson once a week.
Last year I had a few things to work on. A big thing was falling off the mound per say. This was a product of opening my hips to early, and we really worked to get rid of that and stay closed longer. The other thing was to get extension on release and get the my arm out. It helped movement and control a lot.
It was really encouraging experience for me. He was a former 2nd round pick, and I believe he was with the Expos in 94' when they were supposed to go to the world series. He'd throw in little bits from his experiences: One day I was tried to really get an 0-2 fastball outside, and end up in th middle, I remember him telling me about focusing not opening early, cause he did that with a slider to Sosa, only to watch the ball soar over the centerfield wall.
The other big thing was mindset. He knew baseball, and he really knew how to teach a thinking that I would say a lot of guys unfortunately don't pick up. The whole package mentally. Specifically before last year I had never pitched effectively inside. I loved throwing inside this year, moving the feet, and messing up rythm. He really got me to use my movement for disception by starting a pitch towards the middle and letting it run hard on the hitters hands.
I actually ended up working with him from a suggestion by one of my coaches. Basically we have a mega facility in town with multiple instructors and a full size little league field/major league infield indoors. My coached worked at the facility and thought I'd have a good time working with my instructor and I definately did.