If a creature you control is being targeted by a spell when Autumn’s Veil resolves, nothing happens right away. When that spell would resolve, its color is checked. If it’s blue or black, that creature will be an illegal target for that spell, and will be unable to be affected by it. If all that spell’s targets have become illegal by the time it would resolve, it won’t resolve.

Keep in mind that an Aura spell targets the permanent it will enchant (but an Aura on the battlefield doesn’t target the permanent it’s attached to).

Autumn’s Veil has no effect on abilities. After it resolves, spells you control may be countered by abilities from blue or black sources, and creatures you control may be targeted by abilities from blue or black sources.

Autumn’s Veil itself may be countered by blue or black spells. Its effect doesn’t apply until after it resolves.

Autumn’s Veil affects any spells and creatures you happen to control at any point during the rest of the turn, not just spells and creatures you control as it resolves. That’s because it doesn’t grant an ability to those spells or creatures; rather, it affects the game rules and states something that’s now true about those spells and creatures.

After Autumn’s Veil resolves, no new blue or black spell may be cast that turn targeting a creature you control.

After Autumn’s Veil resolves, any spell you control that turn can still be targeted by spells that try to counter it (such as Cancel), regardless of their color. If those spells are blue or black at the time they would resolve, they will resolve, but the part of their effect that would counter the spell you control simply won’t do anything. Any other effects those spells have will work as normal.