Chrono Trigger/The Queen Returns
The Queen Returns (600 A.D. first time)
 Truce Canyon
Enemies: Blue Imp, Roundillo
Items: Tonic, PowerGlove
After taking a bold trip into the unknown, you'll be ambushed by three blue imps. They should die with one hit even on low levels. Continue to the left, kill some more bad guys, to enter a mountain area with two chests (a Tonic in the North West, a PowerGlove near the center); follow the path up, left and then down (go off the path for the chests). Press to open a chest. You'll get into one more mandatory fight with 2 blue imps, and you can fight a couple blue imps kicking a ball back and forth at the exit in the south west (just walk past if you don't want to fight). This will probably be the first fighting you do in the game in these areas (unless you took on Gato at the fair or the enemies in Guardia Forest) so use tonics if you need them and rest in the inn later.
One thing to keep in mind about monster fights in general is that virtually all of them are strictly optional. Meaning if you're fast, careful, or just take the time to avoid them you can skip most of the "random monster" battles most people associate with RPGs. If this is your first run through the game I'd recommend fighting all the regular monsters just to build some levels, but if this is a New Game + you can practice dodging all the monsters. One general tip that comes in handy is that if you stay perfectly still monsters won't bother you, you have to be moving to engage them in battle.
 The Queen Returns
Enemies: Green Imp, Roundillo, Roundillo Rider, Blue Eaglet
Items: Power Tab, 2x Ether, 100 G, Tonic, BronzeMail, ∞x Shelter
Out in the world again, you'll notice it's a little different (mysterious one might say).
 Exploring Truce
Explore the village of Truce: while you won't know the year at first, a woman within the northern residence will soon inform you that it's the year 600 A.D. and Guardia is at war with the mystics. If you nap at the inn, you'll notice a strange black box beside the bed; these will become useful much later in the game. Out on the overworld, you'll also notice that the bridge leading to Porre has now been seemingly destroyed... Whenever you're ready, head into Guardia Forest to the west (just south of the castle).
Within the forest there are many enemies waiting to ambush you, both on the trail and within bushes. Note that there are six possible battles, if you take the left path you will only be required to fight three Blue Eaglets. You can interact with bushes by pressing ; but remember that there is only one bush that you'll get a Shelter from, the rest will turn out to be fights (if you want more, then reenter the map and grab it from the same bush). Make sure to get the Power Tab at the bottom right area within the grassy patch (on the northern side); you'll have to fight two Roly Riders if you get close to the bottom shiny spot next to the rock. Head North to reach the Castle.
 Guardia Castle
As you enter you will be made fun of by the guards, who then get talked down by a familiar-looking queen. Explore Guardia castle if you like, you can restore your health in the knight's quarters to the west (talk to the woman by the bed), or the kitchen to the east (stand in front of the north west chair and press while facing the table) where you can pick up an Ether within a chest by the cooks. Note that the cooks give you a choice of what to eat: Refresh Salad which refills MP, Power Stew for HP and Hyper Kabob for both HP and MP. Eventually you'll want to head north, talk to the king, and head to the north east to visit the queen. You can talk to the chancellor before or after you visit the queen, he'll say slightly different things. If you talk to him before, he'll say "Hm..." and walk up the stairwell in the north west. Follow him up, grab the 100 G on the third floor and then talk to him at the top. He's acting very strangely, as everyone else has noticed. Head into his room where you can pick up a BronzeMail, equip it and then head back down.
Head upstairs to the Queen's Room (north east or right stairwell), grab the Tonic on the 3rd floor, continue up and head south. Talk to the guard blocking the entrance, then continue into the room. Grab the Ether behind the chair. You'll find out that Queen Leene is actually Marle. She'll thank you for coming for her, then suddenly teleport (notice the blue sparkles that appeared when Crono used the Telepod). Try to exit the Castle and Lucca will show up and explain that Marle is actually princess Nadia, and that Leene is her ancestor (although graphically they display her as being Nadia's Great Grandmother). Leene was going to be rescued, but they called off the search now that Marle was found. The problem is that if Leene is never rescued, Marle will cease to exist, so you and Lucca head off to rescue her. You can talk to a few people in the castle for clues or Toma in the inn (he enters after several seconds). Make sure you grab the BronzeMail in the king's room before you leave.