After you escape from the robots in the factory, you reach the End of Time.
Explore the End of Time
Go east and talk to the man at the lightpost.
Whenever you want to change party members, just press Y. You can change members any time you want, from anywhere and time period in the world, except during battle.
There is a save point to the left, and a sparkle above it. Check on the sparkle above the save point to heal up, then use the save point if you wish to save the game. Don't check on the sparkle northeast of the old man unless you are ready to battle the final boss.
Try to leave, and the old man will call you back. Talk to him, then go north into the next area.
Talk to the monster. Then walk up against the left side of the door frame, then go west while staying in contact with the wall, then when you reach the corner, go north while staying in contact with the wall, then when you reach the corner, go east while staying in contact with the wall, then when you reach the corner, go south while staying in contact with the wall. Then repeat the process two more times. Afterward, talk to the monster again. If you did it correctly, you will learn magic. Spekkio will ask if you want to try it out, and if you say yes, you will battle him.
If your Crono's level is less than 10, Spekkio will be in the form of a frog, and you can get a Magic Tab if you defeat him. If Crono is already level 10 or higher, Spekkio will be in the form of a Kilwala, and you won't be able to get the Magic Tab from defeating Spekkio's frog form.
If Spekkio is in frog form, you will already be at a good level to fight him. All physical attacks miss, so be sure to only use your new magic abilities. If Spekkio is not in frog form, don't try to battle him until Crono is level 19.
Switch your other member into your party and talk to Spekkio to unlock their magic. Then leave the room.
Talk to the old man again.
Go west to the pillars of light. Use the middle pillar back to Proto Dome. Walk around in front of the Gate until you hear a sound, then pick up the Power Tab that appears.
Then use the Gate to go back to the End of Time, and use the northernmost pillar to return to 1000 A.D. You will arrive in a different part of the world from the one you came from.