The first method is to make a transaction on the Bitcoin ABC chain that sends all of your coins on that chain to another address in your wallet. This transaction would use their newly-defined sighash type which is invalid and unknown to the non-ABC chain. Once that transaction has confirmed, send the coins on the non-ABC chain to yourself as you would normally.
The second method is to make a transaction on the non-ABC chain which includes an OP_RETURN output with the string
Bitcoin: A Peer-to-Peer Electronic Cash System
The third method is to use transaction lock times. On the chain that is longer, create a transaction which has a sufficient fee to be confirmed in the next block or two and has a locktime of the current block height. Once that transaction confirms, on the shorter chain send your Bitcoin to yourself as you would normally. Note that this method requires on chain to be several blocks longer than the other chain.
There is actually a fourth method that uses RBF, but I don't know how well that would work since Bitcoin ABC removed all RBF logic.
Note that all of these transactions must be transactions back to yourself. That way if you made a mistake and a transaction is replayed, you won't lose any coins.