Try something like this for contracts that need constructor arguments
var bytecodeWithParam = MyContract.new.getData(
param1,
param2,
{ data: compiledByteCode });
It is this bytecodeWithParam that you paste into the "Byte Code" field. If you look at it in detail, you will see param1 and param2 32-byte packed at the end.
Another Example
var MyContract = web3.eth.contract(abiArray);
// instantiate by address
var contractInstance = MyContract.at(address);
// deploy new contract
var contractInstance = MyContract.new([constructorParam1] [, constructorParam2], {data: '0x12345...', from: myAccount, gas: 1000000});
// Get the data to deploy the contract manually
var contractData = MyContract.new.getData([constructorParam1] [, constructorParam2], {data: '0x12345...'});
// contractData = '0x12345643213456000000000023434234'