Before I start, I want to mention that the whole concept of improvisational piecing is wide open to interpretation. Different quilters interpret improvisation in different ways. There are all kinds of tips and tricks out there, but I don't think there's any one "right way" to do it.
For me, this is an improv project because I'm starting without a pattern, only a loose plan. It means that I plan to approach each block as a fresh part of the project and not worry too much about precise angles and measurements.
Once I knew what fabric I was going to be working with, I made a quick little sketch of a block design. No measurements or anything like that -- just a quick little sketch.
My main ideas for this block were a) framing the bird cutout in Ivory, b) vertical strips on the left side of the block, and c) using that dot piece in the upper-right corner. I started by piecing those three components of the block.
The only measuring I plan to do in this project is squaring up each block with my 15" x 15" ruler. Unfortunately, when I went to square up this block, I found that it wasn't quite big enough. I suppose that's the downside to not measuring!
I should note that, when I refer to "squaring off" an edge, I don't mean that I'm making that edge square (i.e. at a 90 degree angle) with the sides of the block. I just mean that I'm creating a straight edge along which to sew. My "squared off" edges are all at slightly random angles.