To the best of my knowledge, all synagogues are organized along the same basic lines that IBender laid out, regardless of what 'stream' they are (Orthodox, Conservative, Reform) And as Kitty said it is REFORM, we haven't been reformed.
I was raised Conservative, and now worship at a Reform Temple. We are a small, semi-rural Temple - 40 member families, so we can't afford a full time rabbi, instead we are served by a student rabbi from the Hebrew Union College who comes one weekend a month. Occasionally a lay member of the congregation leads services when the rabbi isn't in town.
It is just as common to find women serving as rabbis and cantors, and board members, as men in Reform synagogues. It took longer for the Conservative stream to get comfortable with this concept, but women are making inroads there too.
To the best of my knowledge, once you get the the Orthodox, you will not find women in any position of leadership outside of the religious school.
I'd like to say that the Rabbi sets religious policy, but in some congregations (Reform and Conservative) the Board may take the Rabbi's requests 'under advisement' and leave the finally policy to the Ritual Affairs committee (which the rabbi would usually be on)
My understanding of Orthodox synagogues is that the Rabbi is the most important person, setting policy not just in the synagogue, but community standards as well. (Google- Williamsburg, NY)
Smaller congregations also don't have the funds for a paid cantor who leads the singing/chanting of prayers, but many have a member who acts as a cantorial soloist who fills this role.
Most average size congregations have 1 rabbi and 1 paid cantor. It really depends on:
1.size of congregation
2. socio-ecomonics of the area the synagogue serves
3. what other services the Temple provides. e.g - do they have a Jewish Community Center? (which can be similar to a YMCA, lots of variety here), Do they operate a Jewish Day School? (Think of it as a Parochial school for Jews) Do they run a soup kitchen? etc. Organizations of this scope would of course involve much more organizational hierarchy, but I don't think this is what you are asking!