Getting yourself elected to Parliament (Australian Federal).
Step 1. Are you qualified?
At it’s simplest you need to be 18 years old when nominated as a candidate, be an Australian citizen and eligible to vote.
There are fairly usual qualifications about insolvency, metal illness, convictions for treason, being in the pay of the Government and being a member of any other government.
Qualifications and disqualifications - PEO
Our youngest MP is Wyatt Roy who was 20yo when elected in 2010 and it was the first election in which he was entitled to vote.
Many of these citizenship questions were problematic at the time of Federation. Naturally enough, most of the first parliamentarians were either native born or UK born but were British citizens. This was not considered then to be a “foreign power”.
Chris Watson, Australia’s 3rd Prime Minister and first Labor PM was almost certainly a Chilean citizen by birth rather than the Kiwi (and hence a British citizen) most thought he was when he immigrated aged 18.
However the question came to substantial prominence more recently on the arcane aspects of dual citizenship, in some cases by birth, in others bestowed or inherited.
The question asked by most political parties of their prospective candidates during the selection process was simply “Do you have Australian citizenship”. If “Yes”, then that was the end of the matter.
In 1988 Heather Hill was elected as a Senator for Queensland. She was born in the UK but had become an Australian citizen before her nomination. She renounced her UK citizenship after being elected. The Court of Disputed Returns ruled that she was subject of a foreign power when nominated and she was disqualified from taking her seat.
The warning shot was generally ignored. Then in 2017 it really hit the fan.
Green Senators Ludlam and Deputy Leader Waters resigned when it was discovered they held dual citizenship (NZ and Canadian respectfully). The major parties chuckled over the Greens ineptness to lose 2 of their 5 members. The PM berated the Greens for being “careless”. But that was just the start of the can of worms.
Senators Roberts (UK citizen on basis of being Indian born) and Nash (Sydney born with a Scottish father was UK citizen by descent) were referred to the Court of Disputed Returns. The laughing stopped.
The HoR Deputy Prime Minister Joyce, and leader of the National Party was also referred as, though Australian born to New Zealand parents, he was considered by NZ law to be a New Zealand national.
The election of Senator Canavan was disputed on the grounds, though of Australian birth he held Italian citizenship bestowed through his Australian born mother who was granted Italian dual citizenship in 1983 after he was born.
The election of Senator Xenophon was disputed on the grounds he held British Overseas Citizen by descent due to his father being born in Cyprus. To add to the irony, his father had been a partisan who fought the British for Cypriot independence.
At this point the Court of Disputed Returns (who are a special jurisdiction of the High Court of Australia), who were popularly thought to be pragmatic, recognise that there would likely have been a lot of these instances in the past century and sweep it under the carpet, didn’t disappoint. 
The Court noted that the Constitution [s. 44(i)] draws no distinction between foreign citizenship by place of birth, by descent or by naturalisation. They rendered the elections of all but Canavan and Xenophon invalid. 
After this ruling a further 3 Senators resigned (by this stage there were smart alec questions being raised about whether the elected Senate was able to raise a quorum) and another HoR
A register was established for parliamentarians could declare their bona fides including the their place and place of birth, their citizenship status at the time and the place and date of birth of their parents and grandparents.
Then to show that some MPs really couldn’t read tea leaves, the wind or even newspapers HoR Feeney resigned when he could not produce any evidence of renouncing his UK citizenship and Senator Gallagher who had taken action regarding her UK citizenship but that renunciation had not become effective before her election was disqualified.
Political parties ask a lot more questions nowadays. 