Many first home buyers pay no transfer duty at all. Whether you do depends on the value of the property and on whether you are buying an established home or vacant land.
You apply through the first home owner grant application either way, including for an established home. That one application covers both benefits. The grant part is only available for a new home. The duty concession applies to an established home as well, so buying established gets you the duty benefit on its own.
If you are borrowing, your bank or broker usually lodges the application. If you are not, you lodge it yourself. Get your documents to them early. If the approval is not through before settlement, duty is assessed at the general rate and you pay it at settlement, then claim a refund once the approval comes through.
RevenueWA publishes the current rates and thresholds and who is eligible. See also First home buyers: what happens at settlement in WA and Don’t get stung by the duty lodgement deadline.