True, downtown Brooklyn isn't the best place to park. The advice above to park in Park Slope or Bay Ridge is good.

Park Slope is the closest option. Park on the side streets near 4th Ave. It's just street parking so you'd have to look around for a space. The further South you ago, the easier it will be to find a space. Also a ton of great places to eat in Park Slope if you want to get there earlier. After you've parked, you can either walk up to Atlantic Ave (around 15 mins), or take the R train (or N if it's running local on the weekend) a few stops to the Barclays Center.

It's probably easier to find a parking spot in Bay Ridge, but it's farther away. Again, park anywhere near the 4th Ave R train stops (69th, 77th, 86th, 95th Sts), and take the R train up to Atlantic (switch to the N at 59th St if it's running express). Should take about 25 to 30 minutes on the train.

There's plenty of free parking spaces, as Park Slope and Bay Ridge are more residential areas.

And most people would suggest New Yorkers to not drive to Barclays Center, but I think it's not a bad option for people who live outside of the New York metro area (especially in Central Jersey) to drive. Taking the train to Manhattan, and having to transfer to the subway just seems like a really long way to get to Brooklyn from where you are.