Well, in the US those who don’t vote may be a majority or a near-majority, but this would not be true in most democracies. Democracies with voluntary voting mostly expect a turnout in the 60%-85% region in elections, so the non-voters are a sizeable minority, but not a majority. I would guess that most democracies where voting is compulsory would expect a turnout in this range if voting were voluntary, rather than a turnout of US levels.
The theory, I guess, behind compulsory voting is that voters who would otherwise abstain will be forced to engage with the issues in the election, and will actually form and give effect to views on the candidates or their policies. Presumably there is at least a proportion of voters who do this. Others spoil their ballots in protest at having to vote (do Australian elections have a higher proportion of spoiled votes than others?). Still others vote more or less at random (the “donkey vote” for the first candidate on the ballot paper).
How do candidates try to appeal to them? Well, even where voting is voluntary candidates will often try to bribe voters, not individually but collectively by promising to deliver roads, hospitals or other public expenditure to the constituency, so asking the voters to vote for them for material reward rather than because they approve of the candidate’s ideology or policy, or because they trust his integrity and judgment. Is there any evidence that this happens more in elections where voting is compulsory?
A more sophisticated strategy might be to try to identify the kind of voter who wouldn’t vote if not compelled to, and to find out what does interest them, and try to appeal to that. Is the area football-mad? Present yourself as a keen football supporter, and a diehard fan of the local team. Your hope is that the reluctant voter will think “well, I don’t know much about politics, but I have to vote and this guy seems like me, so I’ll vote for him.”
Unfortunately I’m not close enough to Australian politics to know how candidates campaign, and to speculate about how that might be affected by compulsory voting, and I don’t know of any other country where voting is compulsory.