Step 1: Beat Lavos. This will unlock the Dimensional Vortices in 1000 AD, 12000 BC, and 2300 AD.
Step 2: Beat the three Vortices. (You'll know when, there's a boss at the end of each... Although 1000 AD has two bosses)
Step 3: Go to the End of Time. Gaspar will say some interesting stuff, and you can now access Time's Eclipse, a.k.a. the Darkness Beyond Time, from the bucket that normally leads to the Day of Lavos.
Step 4: Go to Time's Eclipse, watch the scenes, and defeat the uber-powerful boss waiting there after picking up your jaw at what it looks like. O_O
After that, enjoy the ending! However, the boss is EXTREMELY powerful, I'd recommend being in the mid sixties at least with a party of Robo, Crono, and Janus. (Robo equipped with his new ultimate weapon, found in the 2300 AD Votex -- it's very well hidden, though, as are a lot of other nifty items. I'd recommend using the maps someone submitted here a while ago... Trust me, though, you barely stand a chance without the new weapon. Dragon's Tear helps too, if you've done the Lost Sanctum quests) Haste Helms, Nova Armor, and Golden Studs on all would be my recommendation for equipment, with a Dragon Tear for Robo (because trust me, you will need the critical hit % boost for his weapon...)