You can follow the Burrwell instructions for a Shield. The parts are so similar, even though differently sized, that it corresponds directly.
A few notes:
Looking from the rear of the gun, the rear (and front) site is removed from left to right. The photo is correct; the written description is not.
The focus of the Burwell trigger job is to:
Reduce over travel
Reduce trigger reset distance
Reduce trigger pull weight
While these are desirable, they do involve permanently altering some parts by cutting or reshaping. This is not beginner stuff.
My first Shield trigger job was aimed at smoothing a very gritty and even unpredictable pull. I polished all engagement surfaces without removing metal. I got a lower pull weight and a smoother, more predictable pull. It was simple and fast.
Next, I really attacked the striker block—mistakenly referred to in the Burwell text as a firing pin block. In extensive polishing of the lower engagement surface I did round the edge that contacts the trigger bar somewhat more, and this is beneficial.
However, my trigger pull was still gritty after all this polishing. The only area I had not touched was the striker block channel in the slide. This turns out to be, at least in my experience, the greatest contributor to the gritty pull in the M&P line.
The tool that drills this channel, even though sharp, can leave burrs at the intersection of the block channel with the striker channel. As well, the striker block channel may have imperfections from the tool.
With the slide completely disassembled, run a small dowel up and down inside the striker block channel to feel the rough edges and intersections. Use 1000 grit wet/dry paper, wetted, wrapped around the small dowel to polish both the striker and block channels, including the intersection, until the bare dowel test indicates they are smooth. Then polish the outside circumference of the striker block. Reassemble with a light coat of grease on the striker block.
This is not too challenging and will make a very big difference in smoothing the trigger pull and in reducing the perceived weight of the trigger.