What information would I need to discern my true input to the transaction from the mixins? Can this be easily done?
Every transaction declares a key image for each ring of outputs being spent, where that key image relates to the true output being spent.
The only way to know whether that transaction is spending your output is to check whether any of the key images declared are key images for outputs you've previously received.
The only way to know which outputs you've previously received is to scan the entire blockchain for any outputs destined for your wallet.
Since explorers typically will not replicate this 'wallet-like' functionality for scanning the entire blockchain with your private view key to discover outputs you own, this would not be possible to do with an explorer.
If you have previously used a wallet to discover which outputs you own, you could make a note of the key images of any outputs you own (this requires knowledge of both your private spend and private view keys). You could then compare those key images with those presented by an explorer.
As @knaccc points out, you cannot do this with just a web based blockchain explorer. However, using the command line wallet
monero-wallet-cli, you can quite easily determine the output(s) you used to fund the tx as inputs. In the
<txid> with your actual txid), will show you your output(s) spent and the indexes of the decoy ring members.