Land at the Accessory Shop and talk to Pinnochio. Use Trinity Ladder #2 to gain access to the Synthesis Shop at last! Check the two Chests for a Mythril Shard and Dalmatians 7, 8 and9 then check the note next to the fireplace for a Postcard . Now you can talk to the Moogles to learn how to Synthesize. You should be able to make quite a few things at the start. Mail the Postcard for an AP Up and you can head to the next world or revist worlds to gather the rest of the available items. It also might be a good idea to visit the 100 Acre Wood.
You can put out the torches around the area with Blizzara to receive a Holy-G and there is Trinity Ladder #3 near the rankings that gets you a Mythril .
Land at the Rabbit Hole to use Trinity Ladder #4 and receive an Elixir . Go to the Bizarre Room and shrink down. Trinity Ladder #5 can be found in the chimney, use it to find a Chest with a Mythril Shard inside.
Disembark at the Jungle Tunnel and climb to the Treetop. Use Trinity Ladder #6 to acquire a Mythril Shard and plenty of green orbs.