You need to understand there's two software pieces at work.... Armory relies on bitcoind (nominally, Bitcoin Core) for it's block history and transaction and block validation.

You'll need to download the hardfork node software (BitcoinABC I believe it's called), create a copy of your existing bitcoind data directory, and configure bitcoinABC to work against the copied data directory.  I would expect (as much as I expect anything in bullshit-hardfork-land to work) that bitcoinABC would start up, validate the blockchain, hit the point where they hardforked, then reach out to the network and fetch the new hardfork blocks.

Once the new bitcoind is synced up and happy, you'll need to take a copy of your armory environment, and point that copy at the new bitcoind. That will let you see your balances on the BCH chain.  Note that Armory is currently not capable of creating valid BCH transactions, so you will not be able to spend the coins yet.

You need to be very careful here. Ideally you want each of these pieces running in its own VM.  If you run a misconfigured bitcoinABC instance on a machine with a normal Core installation, bitcoinABC will munge Core's data directory.  Likewise, if you take an Armory instance and flip-flop it between Core and ABC, you're likely to break Armory's understanding of history and will have to re-scan the blockchain to have a correct transaction history and spendable balance.