If you and someone else both send money to Wikileaks, you both sign your transactions. The transactions, even for identical amounts, are not identical. For one thing they will name different unspent txouts to spend; for another they'll have different timestamps. For a third thing they will specify different addresses for "change" to come back to. All of these things will be combined in a hash function to give your transaction a transaction ID which is unique.
There is no way in a transaction to determine what is "my output" and "your output". That is what makes coin join work, but also brings up the problem originally posed.
Your output is the one that you have the key to spend. What's hard about that? There may be no way for anyone *else* to tell whose output is whose, but you are the guy who created that key pair, you still have the private key, and you know damn well whether a given output has the corresponding public key. In a coinjoin everyone can identify their own outputs. But they can't distinguish anyone else's, and no third-party observer can distinguish them at all.