When you're talking about someone's job, you say that they "work for" an organization or "work at" a company:

She works for the government.

Don't you work at Google?

When you talk about someone volunteering for a charity, you say that they "work with" the organization:

I've worked with the Youth Arts Council for over 15 years.

You can also use "work with" when you're talking about jobs that help people who are disadvantaged:

My dad works with troubled teenagers.