Total noob question on startup private equity

[Sotiria]

I don't even think "private equity" is the correct term, but here goes anyway:

Say I'm a part of a startup. I, along with a handful of other people are doing the grunt work to make this company take off. I believe that the company has a huge potential and believe in the vision that the principals are sharing. How do I go about "investing" in my own company so that as we become more profitable, my "shares" in the company gain value.

Again, not sure if my question makes sense, or if I'm even asking the "right" question but hopefully someone can steer me in the right direction. Currently there isn't any way to "invest" but I'd like to know what I can pitch to the owners.

Thanks.