While the best indicator that the chain is long enough most times is a nice S pattern in the rear derailleur is is still best to re-size the new chain using the old chain as a guide.

Reason for this is even though the chain may appear to be sitting on the gears correctly. It could still provide some issues when shifting into certain gear combinations by there being too much slack in the chain.

If you want there is a really good alternative method of sizing a new chain taught via bicycletutor at http://bicycletutor.com/calculate-chain-length/. Though even he still recommends replicating the same length as the old chain if you still have it.

As for chain tools if you don't have one already they are dirt cheap as most LBS's and shouldn't cost you more then $5. Even though you don't need one after you've sized the chain and have a quick link they are still nice to have in your tool box just in case.