I skim the prospectus summary before skipping to the financials (index to consolidated financials) and the notes below them. (The notes are where red flags are hidden.) I then skim the description of capital stock, principal and selling stockholders and related party transactions for scumminess.
Finally, if nothing there looks off-putting, the MD&A. (If management is screwy, the MD&A is easier to manipulate than the above sections.)
Business section will go over the history of the company, the product, high level strategy etc. MD&A will include all of the financials and provide some commentary
At the front of every S-1 is the "Prospectus Summary" [1], which is easily identified as it has a black border around it. It's a condensed version of the rest of the filing, so (a) it may have some parts that don't interest you, and (b) it repeats information that is explained more fully in other sections.
My recommendation is to check out the Table of Contents [2] and click on a few of the sections that stick out to you. Every S-1 follows the same format [3], so if you skim through one of them you'll get a good idea of what will be in others and what you care about.
When I'm primarily interested in learning about the business (i.e., not making an investment), I head straight to the Business section [4].
The MD&A [5] is also great. You'll learn additional things about the business, but it will be mixed in with financial data. A lot of that detail might not be important to you. For instance, there are sections of the MD&A that discuss non-GAAP financial metrics (i.e., financial metrics that are not standardized by the SEC) or the company's liquidity. The headings within the MD&A help a lot.
The Risk Factors [6] can be interesting, but there's a lot of boiler plate info. Skim it and look for things that seem specific to the company. For instance, there's one that says, "The markets in which we participate are competitive..." and it lists companies they see as their competition. A couple pages later is one that says, "We target enterprise customers..." and has some details on customer size and concentration. But then there is one that says, "If we fail to retain and motivate members of our management team or other key employees, or fail to attract additional qualified personnel to support our operations, our business and future growth prospects would be harmed." There are some specifics about the company and the market they are in, but it's also kind of obvious and in there so that a shareholder can't sue them later and say, "We didn't know this was a risk!"
I hope this helps some. It's a bit daunting to see so many pages with so much information. Happy to answer other questions you have. I took a few companies public as an investment banker, then invested in equities at a hedge fund, and also have a PhD in capital markets and disclosure.
[1] https://www.sec.gov/Archives/edgar/data/1734722/000119312521...
[2] https://www.sec.gov/Archives/edgar/data/1734722/000119312521...
[3] https://www.sec.gov/files/forms-1.pdf
[4] https://www.sec.gov/Archives/edgar/data/1734722/000119312521...
[5] https://www.sec.gov/Archives/edgar/data/1734722/000119312521...
[6] https://www.sec.gov/Archives/edgar/data/1734722/000119312521...