Create an API token with the "Cache Purge" permission for the zone, then:
curl -X POST "https://api.cloudflare.com/client/v4/zones/$ZONE_ID/purge_cache" \
-H "Authorization: Bearer $CF_TOKEN" \
-H "Content-Type: application/json" \
--data '{"purge_everything":true}'
The zone ID is on the zone's overview page in the dashboard. To purge just a few URLs instead of everything:
--data '{"files":["https://example.com/","https://example.com/garden"]}'
I run this from the deploy script, right after the build finishes, so a deploy never leaves stale pages at the edge.