People in the poly community will often tell you that the #1 requirement for a poly relationship is communication.
That's true, as far as it goes, but it's not really the most important rule of making polyamory work. It's vital, it's absolutely necessary, but it beginsa bit before that.
There's one lesson about poly relationships that really ought to be Rule #0; it is, in my experience, the single most important rule of any poly relationship, but also the one people--even people with lots of experience--most often screw up:
Let your relationships be what they are. Do not force them to fit a shape that is not natural for them. Do not box them, cage them, or try to impose an arbitrary form on them.
You see poly people make this mistake all the time. It may take one of several forms.
The first, and most common, is attempting to enforce an arbitrary distinction: "I already have A Primary Relationship(tm), so I will make sure that from now on I have only Secondary Relationships(tm)." Just as it is impossible to force a casual relationship to be deep, so is it impossible to force a deep relationship to be casual; and trying to do so tends to hurt everyone involved--usually, the person required to be "secondary." (In fact, such an arbitrary distinction tends to be rather cruel on anyone coming into an established relationship; when it works, it works by accident, not because the structure makes it work.)
The second, only slightly more common, version of this mistake: "I'm poly, but I absolutely will not let my partner see anyone who is not seeing me as well. Anyone who wants to date one of us dates both of us." In real life, outside of Hot Bi Babe(tm) fantasies, relationships and connections form between different people at different rates, and relationships take on different shapes; expecting a relationship involving three people to develop at the same rate and in the same way all around is kind of foolish. In fact, those couples rarely find their Hot Bi Babe(tm), because real-life Hot Bi Babes(tm) want to be treated as human beings, not as sex toys and not as pets. (It often seems that the couple searching for the Hot Bi Babe(tm) wants someone willing to pack up and move across the country to be with them, promise not to make any waves or upset any applecarts, and who will go away without a fuss if he or she becomes a problem.)
Another classic mistake people in poly relationships often make: Expecting newcomers to the relationship not to change anything, not to make any ripples, and not to have any real impact in their day-to-day lives. Such people want external relationships provided they are tidy and convenient, but God help anyone who has any real needs! However, that's a rant I'll save for another time.