How was the blockchain's "hard fork" automatically resolved?
The highest blockchain containing only valid blocks is always the "correct" blockchain.

The first 225430-block was accepted by 0.8 clients/miners, but due to a flaw in 0.7 clients/miners couldn't accept the block.

The 0.7-fork was accepted by all client and miners, and the 0.8-fork was only accepted by 0.8 clients/miners. The core Bitcoin developers decided they wanted the 0.7-fork to be highest, however 0.8 had the most mining power, so the developers asked mining pools to switch back to the 0.7 client.

After some time, the 0.7 blockchain (which didn't have the "flawed" transaction) was highest, and 0.8 clients/miners would treat this as being the "real" blockchain (and stop mining on the blockchain with the transaction 0.7 clients didn't accept).

The 0.8 fork is simply treat as many orphaned blocks and is not worth anything (it can't be spend, etc).