Congratulations, you've just beaten the game. Enjoy the lengthy ending, but don't pack away the game just yet. You can continue the game and complete one more dungeon to "graduate" from the guild, the Mystifying Forrest. This isn't a very difficult stage, but at the end, you'll need to fight all of your friends from the guild, and since you can't have recruits with you, this will leave you quite outnumbered. Once you beat this you will have access to the Luminous Spring, which can be used to evolve your recruits. You won't be able to evolve your main Pokemon until after you recruit Palkia (who, in turn you can only recruit after Manaphy has been in your party for a few days).
Now more of the world will be open to you, and Zero Isle will be of particular interest. These very difficult dungeons have special rules. You'll be able to take on missions to explore these, or you can go on your own. Continue to take on jobs, and regularly explore the guild and Treasure Town. You will notice new characters cropping up. The first of these, for example, is Mr. Mime, and speaking with him will give you access to Blizzard Island.
You can also being to recruit Legendary Pokemon during this time. There are a few of these that are guarunteed recruits if you can defeat them, so start with these: Uxie, at Steam Cave, Mesprit at Quicksand Cave, and Azelf, at Crystal Crossing. You can also head south from the guild to the beach at talk to Lapras, who will bring you back to the Hidden Land. If you revisit Dialga, he will join your party as well. Suffice it to say, Dialga is an incredibly powerful companion, and his range makes him perfect for taking up the rear lines. You can also begin to make up parties entirely of recruits, but there are certain dungeons where such parties cannot be used.
After unlocking a new dungeon, the progression is generally to beat it, do missions for 2-3 days, and then find an event to trigger the next dungeon. After Blizzard Island you'll unlock Crevice Cave, and after enough missions you'll notice that there aren't as many Pokemon in the guild. Now head to where your old room was to trigger an event, and a few more days of missions will unlock Dark Crater, where you can fight Darkrai. This is an important event. Manaphy will show up not long after, and you'll be able to recruit even more special Pokemon.
And so the game continues. There is no proper end, but there is a whole lot to explore. Have fun trying to catch 'em all.