I have both my savings and transaction accounts with the same bank (ING), so I can virtually instantly transfer between the two if needed.
I have it set up so that $350 of my (fortnightly) pay goes into the transaction account, and the remainder into the savings account.
I've got a smartphone so transferring money between accounts is super quick, and in a pinch I could get cash from my credit card (but I'd rather not due to interest).
I use the savings account as my emergency fund (and I like to keep at least $5000 there, but currently I don't). All of my bills (except rent) are autopaid with the credit card, and I've got the savings account set to transfer the rent to the transaction account on the day before it's direct debited.