Thanks to Gothamist for some of the info.
Ikea in Red Hook (exactly 13 miles from Continental/Austin) is opening June 18th, ensuring headaches and curse words for all who visit. The store is offering free shuttle service from three nearby subway stops (hear that Trader Joe's?) and a ferry service from Manhattan which tens of people will take annually. There will also be increased bus service for those who weren't made nauseous enough from the crowds and lines inside the store.
Forest Hills 72 recommends the best way to get to the Brooklyn Ikea will be to drive to the New Haven Ikea. Don't have a car? Great - go to Laytner's.
Driving directions in the map above for those silly enough to go. It's exit 26 off the BQE. After exiting, follow the Subaru Forester.