Hello and welcome!
This is a really broad question, so it may be helpful for you to throw out some specific ones and do a lot of reading here on the forum. The life blogs might help you see the wide range of relationship structures within polyamory. I'd also recommend the book More Than Two - fantastic reading on how to "do" polyamory.
In my case, my husband and I opened up our relationship with the original idea of swinging. While my other significant other (OSO), Jack, and I started as friends-with-benefits (FWB), we've developed a strong romantic relationship over the years. We're madly in love with each other! Roger and Jack are good friends, but aren't involved otherwise. In the past year, Roger has been dating his girlfriend, Taylor, as well. We are not involved and haven't spent much time together, though I'd like to get to know Taylor better and see if a friendship forms.
I am not a fan of hierarchical polyamory - meaning that I don't consider my relationship with Roger as more important than my relationship with Jack. I think there's a common misperception for newbie polys that you "have" to have a primary and secondary relationship if you're poly. But it can end up very much hurting people, particularly the "new partner" (e.g., Jack). There is absolutely no "vetoing" of partners - each relationship stands on its own, and there's no way I'd end things with Jack if Roger asked me (and same with Taylor). Just because Roger and I are married doesn't mean his needs come above Jack's - it's a tricky balance.
The way I am poly, I tend to discourage rule setting as much as possible. I believe that Roger and Jack are both independent people and don't need my permission to have relationships outside of the ones with me. I've found rule setting in the past to be indicative of deeper concerns (e.g., insecurity, jealousy) and I'd like (or would hope my partners would like) to grow in those areas instead of using rules to solidify those fears even further. That said, the four of us have agreed to let us all know if there are new partners and to use safe sex practices if so (we're all fluid bonded at this point, each of the three relationships), or one of us has the choice to use protection with the other until he/she has tested clean. We've decided at this time to not come out to Roger's, Jack's, and my families, though that may change in the future (Taylor's family loves and completely accepts Roger

). All new rules need to be approved by anyone that may be affected by the rules. I have frequent check-ins with both my partners to see how things are going. I also have requested in the past to meet my partner's partner (metamour) fairly early in their relationship (e.g., for me - before sex if this seems like a long-term relationship), but I'm more flexible now, have no veto power, and wouldn't ask this of more "casual" (for lack of a better word) relationships. I can't think of any other rules, and ones I've set in the past (e.g., Roger only spending one night at week with Taylor) have been done in service of me needing some time to grow and stretch (no longer a rule). Oh and Roger was completely able to not agree to that, and I can't imagine making that rule in the future.
Hope that gives you a little insight into ONE kind of poly relationship!