I am terribly confused about all this. If Bitcoin splits in to three different currencies by August, and if I am keeping my coins in my Blockchain.info wallet, then can anyone tell me what I need to do in order to claim all three coins? How can I get the private key from the (old) Blockchain.info wallet?
Blockchain.info used to have some way to export your private keys, but I don't think they have that capability anymore. Either way, if you want to be able to use your Bitcoin on all forks after a chain split, then you need to control your private keys and control which chain you are using. Using a web wallet like blockchain.info will not provide you this capability. The easiest thing to do would be to just get a desktop wallet (preferably a full node wallet like Bitcoin Core) and send your Bitcoin to an address in the desktop wallet. Then you will have full control of your private keys and be able to choose the chain(s) you wish to follow.
How about if I have my BTC in a Trezor wallet with a recovery key phrase?
You control your private keys. Which chain you want to spend on only depends on the wallet software you use to interact with your hardware wallet. The hardware wallet itself does not know about nor does it care about the blockchain it is signing transactions for.
Now we are waiting for some guide that will teach us how to save both currencues after the split.
Sure that's what every Bitcoin holder should do. Just in case.
There is actually an amazingly simple way to "taint" your coins that I have only recently heard about. This method requires using transaction locktimes and may require a bit of advanced skill (most taint methods require that anyways).
To taint your coins, you need to make one transaction that is valid on one chain and invalid on the other. Since a chain split will likely result in one chain with a majority of the hash rate and one chain with a minority of the hash rate. The chain with the minority hash rate will produce blocks at a slower rate so it will be at a lower block height. Thus you can make a transaction which has a locktime of the most recent block on the chain with the majority hash rate. This means that the transaction will be valid and can be mined on the majority hash rate chain, but is invalid on the minority hash rate chain until it's most recent block height matches the locktime that you set. Once your locktimed transaction confirms on the majority hash rate chain, you immediately make a transaction which spends the same inputs but does not have the locktime and get that confirmed on the other chain. This second transaction will be invalid on the majority hash rate chain because it conflicts with one that has already confirmed, and if the transaction confirms on the minority hash rate chain, then your coins will be successfully split. You can then spend from those transactions on their respective chains without any risk of transaction replay as any transactions that spend from those will be invalid on the other chain.