How to find contract's address?

For those of you using Parity's trace_transaction call, the newly-created contract address appears in the trace.result.address field. (And, as a side note, any self-destructed addresses appear in trace.action.address while the address that receives the proceeds of the self-destruct appears at trace.action.refundAddress.)

When you are on MetaMask (this is a chrome extension) you can choose the option 'view on etherscan'. Here you can see all the Ethereum transactions.

In the To-address you will see: [Contract 0x........ Created]

You may use "web3.eth.getTransactionReceipt('{txn_id}')". It will give you the contract address as well as other information like block number etc.

You can use a filter to list all transaction from a given address.

var filter = eth.filter({fromBlock:0, toBlock:'latest', address: "0x.."});
filter.get(function (err, transactions) {
  transactions.forEach(function (tx) {
    var txInfo = eth.getTransactionReceipt(tx.transactionHash);
    /* Here you have
    txInfo.contractAddress;
    txInfo.from;
    txInfo.input;
    */
  });
});

You can use an ether explorer like (https://github.com/etherparty/explorer) in your private testnet to look at the mined blocks. These particular explorer show only block info and transaction info. It uses angular and can be modified easily. But currently is somehow "limited".

As jayD has already said, you can set a callback function to be notified when a contract is correctly created.

If you lost the moment, you can anyway retrieve the contract address later. In fact, the contract address is deterministically computed from the address of its creator and how many transactions the creator has sent.

See How is the address of an Ethereum contract computed? for more details.

You're missing the contract address.

When sending a contract for the first time it will return the address to you as a Javascript callback that you said : " Contract mined! address: ........ "

But this is javascript.It will disapear when you closed the browser so you need to save the address beforehand and then call it back at will with :

var MyContract = web3.eth.contract(MyContract.abi);
var Instance = MyContract.at("address");

And you can the use Instance.thefunctionyouwant

You might be able to find the address by checking the last few transactions from your own address since as you said , it is saved forever, but you just don't know where it is. But as it's a test network i would suggest you to recreate the contract save the address and proceed as mentioned.