This page explains how to complete the Cyrus's Ghost sidequest in Chrono Trigger.
Start the Quest
Put Frog in the lead of your party. Go to 600 A.D. and find a previously unreachable continent called Choras. It is southeast of Ozzie's Fort.
Go to the Cafe and talk to the guy who is drinking. He mentions his stolen tools. Then go to Choras in 1000 A.D. and visit the Choras Inn. Talk to the guy who is drinking. He asks you to get the tools from his wife. Go to the Residence in the village and talk to his wife to get the tools.
Go back to 600 A.D. and talk to the guy in the Cafe who is drinking, and give him the tools. Go outside and go to the Residence in the village, and talk to the guy. Then go outside and go northeast to the Northern Ruins. Go inside and watch the cutscene.
Make sure to put Frog in the lead of your party. You may wish to bring Lucca because the enemies here are weak to Fire. Go west, and go down the stairs. Fight the Sentries. Use Fire attacks and do not use Shadow attacks on them. Physical attacks are likely to miss. They use MP Buster when defeated, reducing the MP of the character who defeated them to 0. They may also cast Grudge, dealing a lot of damage to a player.
Afterward, go east, and defeat these Sentries. Don't open the chest to the northeast; its contents will be upgraded if you leave them alone in this era.
Go back the way you came, and defeat the four Sentries that attack. Then go west and up the stairs to the first room of the Northern Ruins. Go east and up the stairs. Go through the door.
You can go west, north, or east. You will need to go to all three paths, so go in whichever order you prefer. Use magic attacks on all of the monsters that you encounter.
After you have cleared out all of the monsters, leave the ruins and go to the Residence, and talk to the builder. Pay him, then return to the ruins, but don't have Magus in your party.
Now go west from the entrance, and follow the path to the end, where Cyrus's grave awaits. With Frog in your party, check the tombstone to start a cutscene. Afterward, the original Masamune is powered up, and is now Frog's best weapon. It is automatically equipped. Be sure to equip the Hero Medal as well.
Now go back to the Residence in Choras, talk to the builder, and pay him again. Then go to the Northern Ruins once more.
Go east and follow the path. Remember not to open any chests. If you see a magical sealed chest, check on it, but don't open it. There are monsters in the north path, including Bases that have a powerful Slash attack. Heal up if they Slash you. Red Pin works very well against them.
When you are done, go out to Epoch and go to 1000 A.D.
Back in the ruins, open all of the chests to get their upgraded contents. There is a Magic Tab to the left of Cyrus's Grave in 1000 A.D., and a Power Tab in the southwest corner of the first room you reach when you take the east path from the entrance. Then, go back to 600 A.D. and open the chests to get the original items.
Also, if you have Frog in the lead and you go to the place in the Denadoro Mountains where the Free Lancer is throwing stones, Frog will catch the stone and you get the Gold Rock. This opens triple tech Grand Dream for Frog, Robo, and Marle.