With my gf it's almost entirely unstated, but essentially that we practice safer sex, honesty, and respect. With my bf, all of the above plus that I not start any new relationships at the time being, and that when we decide together that we're at a place where that can happen we talk about the person in question first and he gets to meet and evaluate them before things proceed.
Me, 30ish bi female, been doing solo poly for roughly 5 years. Gia, Clay, and Pike, my partners. Davis, ex/friend/"it's complicated." Eric, Gia's husband. Bee, Gia and Eric's toddler.