There are a couple ways you can go about this, the most organized and perhaps best way is via CDQ or GCDQ (group character development quest).
However, if it's not something that has a major impact on NPCs or the world in general, say, for something personal, you can use the PvP widget and adjucate the circumstances among yourselves. You could also request a GM watch over the proceedings, but otherwise handle it yourselves.
Really, I think what you choose to do will entirely depend on the situation, and depend greatly on whether the situtation in question (whatever it is the opposing PC is wanting to accomplish that your character wants to thwart) has a significant impact on the world, either locally or on a larger scale.
Feel fee to PM me, or another GM with whom you may feel comfortable, the details of the situation, as we'll be able to offer better advice, more specific at least, knowing what's actually going on.