Matt Bird writes all sorts of nonsense, but he dedicates a large chunk of his time to writing game walkthroughs.
Little Oliver's life has been flipped upside-down. He's lost his mother, his doll's come to life, he's learned that there's a parallel world to his own, he's now IN that world, he has his own wand and spellbook—and moments after emerging, he's under attack.
After the cut scene ends you'll be in battle with a furry little creature called a Ruff. Drippy will guide you through combat, though he won't mention that you can freely move about the battlefield during your turn. Get used to running away from your foe for the duration of its Attack phase, as well as practice with Defend. You'll need to use it in battle every now and then. In particular, you want to use Defend whenever an enemy is flashing, or there are signs of a named attack. These ones hurt more than your garden-variety thuggery.
Head to Ding Dong Dell
Afterward, Drippy will emphasize your need for a better wand than what you've already got. He'll reveal more of Shadar's evil—namely his ability to break hearts—and decide on heading to Ding Dong Dell, a castle so Oliver can begin learning magic in earnest. He'll give you three Loaves of White Bread that will restore Oliver's HP.
You're now on the world map—as good a time as any to save, now that you're in danger of Game Over.
Poking Around the Map
You can head north to Ding Dong Dell immediately if you want, though it's always more fun to poke around. The monsters in the area are no more dangerous than the Ruff, so beat them into submission as they come to you and build up Oliver's level a bit and earn a few Gilders. The only enemy to really watch out for is the Minor Byrde, as they'll use a special attack that can hit hard if you don't Defend the moment they start flashing. Baatenders are the best experience in the region near the castle without going too far out, and they're easier to beat than the Byrdes.
Begin by checking to the east, where you'll see a small, twinkling light—a Bunch of Booster Shoots. They'll be useful when you get into item creation. When you get closer to the castle, check the small mountain range to the northeast for a Plainswort Flower, another ingredient. Far to the northwest, near a small lake, you'll also find a Bottle of Springwater. Almost directly west from the castle on the map is another Bunch of Booster Shoots. There's more, but don't worry about going too far out—you'll be visiting these other areas eventually. Make your way to Ding Dong Dell.
Head to the Deep Dark Wood
The first problem that you'll run into is that the guard here is broken-hearted. He won't let anyone into Ding Dong Dell because he just can't be bothered. Nuts. Drippy says that an Old Man living in nearby Deep Dark Forest can help solve this little problem, and once he does, Oliver will be able to mend any broken heart. Consult your map, then make your way to The Deep Dark Wood.
(Note: If you really like to collect things ahead of time, spend a few minutes killing enemies and hunting down sparkling spots on the world map. An upcoming side quest requires you to have two Bottles of Springwater and two Springwort Flowers, both of which are relatively common items in this area of the map. Have both batches ready for when you eventually enter Ding Dong Dell to make mincemeat of the side quest.)