Same boat as you last spring, Rob. My water was so green I couldn't even see the first step and I just kind of panicked and threw everything in at once, which was definitely the wrong call. What these folks are saying about order is spot on - I wish I had found a thread like this before I started dumping stuff in.
The thing that made the biggest difference for me was actually testing before I did anything. I borrowed a test kit from my neighbor and found out my pH was sitting around 8.0, which apparently means your shock is basically working at like 20% efficiency or something like that. Once I got the pH down and then shocked, the water started clearing up way faster than I expected. I also had no idea you were supposed to run the pump the whole time, so I was turning it off at night like normal and wondering why nothing was happening. Run it continuously until it clears, seriously. And yeah, hold the algaecide until after all of that or you'll end up like poolmom_sarah with a foam situation nobody wants.