Should you find yourself in the position to direct the culture of an organization, congratulations, that means you're at or near the top, you probably founded it, and with that status comes great responsibility.
Your organization's values are going to be an extension of your values. So it's important to know what your values are. Start with a statement of your own values. This should probably be a document of some kind. Start by putting it all down--no one has to read this document, you can be as honest as you like, and the more honest with yourself you are, the better.
Next, write another document, this time the public version of the above. One form of this is the manager readme. Your audience is your organization, and the future members of your organization (employees, volunteers, investors, etc). Your culture will be an extension of your values, so they deserve to know what those values are, but they don't need to know every detail or reason.
Third, yet another document! Writing helps communicate intent much better than talking or hand-waving, and it will help you think about what kind of culture you want and help you hold yourself accountable to live those values and that culture with your future words and actions. This document should describe how the values you described above translate into organizational behavior.
If the value is honesty, this document would describe how someone embodies honesty within the organization. Short narratives are good. Try to pick scenarios that help communicate the intent without being overly specific, so they can be applied in all the different contexts in which people will be finding themselves.
Finally, yes, another document. This one is the practical dos and don'ts. Sometimes this is an employee handbook, but if you're a small organization you probably don't need one of those yet. Just lay out your expectations for behavior clearly so there's no guesswork. Try for more many more dos than don'ts.
Doing all this work early in the life of your organization will help it stay on course when things inevitably get rough, keep everyone united and focused, and help attract the kind of people you want to be part of your team.