How does travelling with dual citizenship work?

Ok so this isn’t for me, but for my grandma.

She’s been an Australian citizen with an Australian passport her whole life but only just recently got a British passport due to new rules and regulations for entering the UK as a dual british citizen, so now she has both Australian and UK passports.

My question is, she travels to the UK somewhat often, what passport is she meant to use when travelling? I’ve heard you’re meant to use the passport of what country you’re travelling to, but the AUS Department of Home Affairs says to use an Australian passport when both exiting AND entering Australia, is this true or should she use her UK passport when entering the UK and her Australian passport when travelling back to Australia?

Any other advice for her would be appreciated :)