I've had two different conversations recently with feminist women who want to start their own tech startups. Even though I have never done that, it turns out that I had things to tell them that they did not already know! NON-ORDERED LIST TIME!

• If you're thinking of starting your own company or nonprofit, check out the books at Anti 9-to-5 Guide (thanks for the rec, Fureigh) and the resources Kronda Adair mentioned at her Open Source Bridge talk "Stop Crying in the Bathroom and Start Your Own Business". If you're specifically thinking about a for-profit product-or-service startup: my friend Rachel Chalmers, a venture capitalist (someone who invests early money into a startup), wrote about why you should be wary of venture capital(ists). You're welcome to reach out to her to pitch your idea. Also read the cautionary words about investor storytime in "The Internet with a Human Face", and some thoughts about less efficient startups.
• If you want to start your organization in order to cause change in the world, have a theory of change. I love that Open Tech Fund tells you what their theory of change is (see the last sentence in their funding model). The Ada Initiative's change strategy is in its FAQ. Here's a sample exercise you can do, courtesy of Wikimedia Foundation's Learning and Evaluation team.
• Remember that you could be a social enterprise -- a mission-driven for-profit company, like Etsy, Growstuff, or Dreamwidth. (Skud, founder of Growstuff, maintains the Growstuff blog and you can, for instance, see a snapshot of its finances.)
• If you are specifically looking to start an organization as a means of increasing diversity in tech, read "Trying to get paid to work on diversity in tech? Read this" and "The Ada Initiative Founders on Funding Activism for Women in Open Source". Consider your theory of change, and look at who's already trying out the method you're thinking about (bootcamps, apprenticeships, online tools, recruiting/hiring arbitrage, after-school programs, training allies, convenings, curriculum change...). And -- as Jessica McKellar entreats us -- once you start trying things, measure what you're doing, so you know whether you're effective.
• If you want to make a product or service that specifically helps people who have mental illnesses, you're not alone -- for instance, at least one person is "Designing an ADHD-friendly to-do app" -- and there's certainly a market there -- for instance, the Compassionate Language Learner, who has depression, uses Lift. And there's a curb cut principle here, where making something that helps reduce anxiety and enhance executive function can help a lot of users, neurodiverse and neurotypical both. One could look at Graze, ZocDoc, and Fancy Hands as models here.
• If you need to improve your own programming skills in order to found effectively, check out the Felder-Silverman learning styles and use your self-assessment to help you choose useful learning activities. If you're trying to choose and stick with learning projects, you may find my piece "From 'sit still' to 'scratch your own itch'" helpful. Maybe you'd enjoy making funny or feminist things. If you've already programmed a bit before, try porting something you already made into a new language. Go ahead and copy existing things that you think are cool, e.g., Hollaback, Listen to Wikipedia. This is learning time and it is OK not to make new things the world needs. You can learn and then build the thing you want to exist. (This helps us see why games are popular learning projects: you have a ready-made specification to work from, so you don't need to decide "how should this work?", and they make people feel happy.)
• If you have not done executive-y things before, check out my Open Source Bridge talk "Learn Tech Management In 45 Minutes".
• If you have, without knowing it, been waiting for someone to give you permission to do this: I give you permission. (No kidding, I said this to one of them, because she realized she needed it. Permission granted!)

I'm sure this is as incomplete as "Here Are Some Grants You Could Apply For" was. Also, as I mentioned, I totally have not done this and websearching around for startup advice from founders will get you a zillion interesting results, and if they contradict me then you should probably believe them instead.