In the 2017 UK general election which has resulted hung parliament, Theresa May is trying to get a deal with the DUP.
If the deal fails, what options do the conservatives have to form a government?
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May could attempt to form a minority government.
The ability of a government to function depends on its ability to win votes in the House of Commons. The DUP may continue to support the government on a vote-by-vote basis, even without an agreement.
As things stand, May has 317 votes (as one of her MPs is also the Speaker, who doesn't vote) There are 6 Sinn Fein MP who don't vote. She needs 322 votes to be certain of winning. She can proceed by consensus, bringing forward policies that she can get a majority to vote for.
If the government loses a vote, it doesn't bring down the government. But if the government loses its budget bill or the vote on its legislative programme (the Queen's Speech), then it can't function and would be forced to resign. If the government lost a vote of no-confidence, they would have to resign. In any case, Jeremy Corbyn could then try to form a government.
If no party can get enough votes to win a confidence motion, then there is another election.
Alternatively, May could attempt a deal with another party. The Lib Dems are the second most likely pairing, the other parties (Labour, SNP, Plaid Cymru, Sinn Fein) are opposed to most of May's policies. And Sinn Fein don't sit in Westminster.