Recap: At the end of Fate/Zero. Karitsugu used his last two command seals to control Saber, and have her use her Anti Fortress Noble Phantasm to destroy the grail. In the Anime it covers Gilgamesh in it's magical sludge and resurrects him. And then grants Kotomines greatest deepest and darkest desire, choosing him as the new victor. Destroying the whole district of Fuyuki that the final battle took place in.
Alternatively (And put at the simplest.): After the granting of Kotomines wish. And the resurrection of Gilgamesh. The grail was in actuality, successfully, destroyed. And the mages Association were none the wiser. Mysteriously, when the grail war seems to have properly begun. The servants are summoned with alternative knowledge: That they are allied with the 6 servants that SHOULD be their foe's. And, are against 7 other servants. This causes complete confusion. And a meeting is immediately called by the main families, of the Association. The mysterious new masters of the grail revealed themselves. And openly challenge the faction of Red. To fight them, and their Black Faction on the new battleground. Paris.