Lucca appears and will help you investigate what happened to the queen.
Talk to People
You can talk to the people in the castle for clues on what to do next. You will learn that the cathedral to the west might be a good place to investigate.
Go to the Cathedral
Go south to Guardia Forest. You may wish to level up until Lucca learns Flame Toss, which unlocks the Dual Tech, Fire Whirl.
Go south to exit the forest, then go west to the cathedral. Talk to the nun by the organ, then check the sparkle.
Defeat the Naga-ettes
Use Fire Whirl on the Naga-ettes if you have it. You can use Fire Whirl on three of them at once if they are close enough to each other.
Afterward, there is a cutscene. Choose to go with the frog. (Default: Frog) Check the organ to reveal a secret door. Go through.
First, go west to find a couple of chests (right: Revive; left: Tonic). Then go west from the chests, then north through the door. Go up the stairs and through the door to find more chests (left: MaidenSuit; middle: Tonic; right: Ether). If you check the dresser, you will find the Secret Naga-ette Bromide, and you will have to fight. Finding this item will give you access to a Tab later on. Exit this room.
From here, go all the way north to find a chest (SteelSaber). Then go west, check the skull to the west to lower the spikes, and go through the door where the spikes were. Check the bucket to find a Power Tab.
Now go back out to the main hall. If you want some money and useful items, go to the east side and go up the stairs. Go north past the first door and go through the second. Ignore the people here unless you want to fight. Open the chests (left: 100G; right: Ether), then go through the wall to the right. Don't talk to any monsters. Go north to find two chests (right: Defender; left: Speed Belt). When you try to go back out to the main hall, you have to fight. Then leave.
Go to the middle of the area and go north up the hallway. You can avoid the monsters here by staying near the rightmost rail of the stairs. Go through the door.
Stand in the sparkle so you can save the game, and use a Shelter if needed, then go north the stairs, go east, and go south down the stairs. Go through the door and check on the switch on the north wall, then go north through the door.
Go west and open the two chests (right: Heal; left: Tonic) and keep going west, then south through a door. Don't use the switch in this room. It just makes more monsters appear. Keep going and you will reach some stairs. Go north up them, then go west and open the chest (Shelter). Once you're back to where you started, you can optionally save and heal at the sparkle, then go north through the door. (If there are spikes in the way, you will need to go back the way you came, to the eastern room that has a wall switch, and press that wall switch.) Defeat the monsters, then open the chest (Iron Sword) and play the organ. Then leave this room and you can either go west or east, then go north to the back hallway and go through the door that appeared in the middle.
If you run north you can avoid the monsters. If Crono and Frog haven't learned the dual tech X Strike yet, you might want to fight until you do. Then save and use a shelter if you need to, and go up through the north door.
Go north and there will be a cutscene, and then you'll fight Yakra. Keep everyone's HP above 50. Have Lucca use Flame Toss, or have her use healing items on people when needed. Have Frog and Crono use X Strike until it dies. Keep in mind that it almost always counter-attacks whenever you attack.
Check both chests (left: Chancellor; right: Mid Ether), then talk to the queen to leave.
Go up to the queen's room (northeast of the throne room) and check where Marle disappeared to find her.
Leave the castle, go south through the forest, then go east to the village, and go north and enter Truce Canyon. Go northwest, up the ladder, northeast, east across the bridge, south and down the ladder, then east to the area where you first appeared. There will be a cutscene, then you will return to Leene's Square.