Peter Russell lays out the options.
When the House does meet and no party has a majority, there are basically three ways of forming a government. First, the Conservatives can simply carry on as a minority government hoping to win support, issue by issue, from opposition MPs. Second, either the Conservatives or the party that finishes second in seat numbers can form a legislative alliance with one or more other parties that would agree to support them on the basis of a shared legislative program. Such an agreement between David Peterson’s Liberals (who finished second to Frank Miller’s Conservatives) and Bob Rae’s NDP gave Ontario a stable minority after the 1985 provincial election. In this option, the parties supporting a Liberal or NDP government would not have cabinet positions. The third option is a coalition government in which two or more parties form a government and share cabinet posts.
All three options are constitutionally legitimate. Indeed, in the dozens of parliamentary democracies around the world, it’s highly unusual for any party to have a parliamentary majority. Governments in most of these countries are either coalitions or single-party minorities supported through alliances with opposition parties.