First you need to check if you are eligible to become an Australian Citizen, the requirements of this, and the costs.
Details can be found here:
Then you need to officially apply and follow the instructions which they issue, pay the fees etc. As part of this process they will ask details of your current citizenships, where you will provide details of your UK citizenship and a copy of your passport (if required)
Assuming your application is successful, then you will officially become an Australian citizen!
You don't need to initially inform the UK of any changes, or that you are now a dual citizen.
However, when/if you apply to renew your UK passport then at this time you need to fill in the section regarding "other citizenship(s)" (the exact name may vary), where you will have to fill in details of your "new" Australian citizenship.
There are no additional fees associated with this.