Boil the the asparagus for 2 minutes, then dunk in an ice bath for 2 minutes (if you want them to look great, if you just want them to taste good you can skip the ice bath)
Sautee the mushrooms in olive oil on high for about 5 minutes, tossing occasionally until dark brown, throw in the garlic and turnip and toss a couple times more
Cut the asparagus into thirds (cut on an angle if you want them to look neat)
throw everything in a big bowl, dump on the vinegar and toss til everything is good and coated.