I would suggest that you start by grabbing a stack of post-it notes and a pen, or stand in front of a blank whiteboard with a pen. Or both, if there are lots of things you want to change.
Brainstorm. Write down every single thing you can think of that you want to change, without thinking much about whether each thing is reasonable and when. Don't worry about it looking silly; some things will, especially a few minutes after writing them down, and that's okay. There are no stupid ideas at this point.
Once you have a large stack of raw ideas, break up and consolidate points as appropriate. Only after that do you start worrying about sorting them (by priority, practicality, cost, or whatever other metric makes sense in your particular situation). Cull the ones that are clearly not reasonable but keep the ones that might be reasonable particularly in light of your overall goals.
The result will be a very rough first draft outline for what to do and in what order. Once you have this first draft, you need to flesh out each point somewhat. The goal here is simply to make sure that someone else reading the document will have some idea of what you want to change and how implementing the change will benefit the business. Specifically, you do not want to spend much time at this point thinking about how to implement the change.
Once that is done, you will have a rough draft that you can take to management to get approval on in general terms before you start figuring out how to approach implementing each individual change on the list and where the interdependencies might be. Especially because you are new to the company, you want to take the document to management and get approval on it in general terms before you spend too much time figuring out exactly how to change points that may or may not be in line with the company's overall business plans. At that point you may want to look at methodologies such as for example Six Sigma suggested by JJosaur in a comment to the question.