Greenleaf’s map is a little complex- not only is there the curious little raised area that Motonari’s army starts in, there are four tunnels hidden in the patches of thick grass, which will transport Pokemon at the end of their turn to a particular other grass patch.
The tunnel just to the left of where your army starts leads to the matching entrance off to the right, near the furthest-right banner. This first tunnel is not terribly convenient, only cutting one move-distance at most from a trip that you shouldn’t need to take anyways.
The darker patch near the central banner connects to the dark patch just beside the rightmost banner. This can be very useful not only for capturing that one of the two further banners, but also for returning from it if you need backup near the central or leftmost banner. Keep your eye on this tunnel, too, as the local army likes to abuse it a bit when they can.
The two light patches immediately in front of your army on opposed sides of the rose-hedge are connected, which can be convenient if you want to start by snagging the leftmost banner and one of your Pokemon is lagging behind the others a bit.
The fourth and final passage is really of no use to you in most situations- it connects the plateau that the enemy army starts on to the lower area nearby, which can bring them to the furthest-right banner and the tunnels near that. That is the other tunnel that your opponent will try to take advantage of, so make sure you park a Fire-type near that rightmost banner to punish him for it.
Be wary of traps, though- several pits have been planted near some of the banners, and falling in a pit wastes your attack opportunity, and the entire next turn for that Pokemon as well. I strongly recommend saving before moving a Pokemon up to a banner, so that you can avert this annoying diversion- though you don’t have to, as it will only hinder you unless you’re incautious enough to drop several of your army’s Pokemon into pits simultaneously.
Keep an eye on the cattail-like reeds as well- while you can stop a Pokemon in their space, and that Pokemon can then attack from it, they will afterwards be launched through the air somewhat randomly. Don’t rely on a Pokemon staying there, though, and you can use it as a small defensive advantage.