Delegating DNS without breaking everything
Every registrar has two screens that look like they should be the same thing and are not. One manages individual DNS records — A, CNAME, TXT — for the nameservers you're currently using. The other lets you change which nameservers you're using at all. Only the second one is nameserver delegation.
I found this out by opening the wrong one first. My registrar's records panel, on noticing I clicked into it, offered to "fix" my setup by resetting me back to its own default nameservers — the exact opposite of what I was there to do. Declining that dialog was the correct move; the actual delegation screen was a separate link entirely, one level up in the domain management view.
Once I found it, the change itself was two lines: swap the registrar's nameservers for the new provider's, save, and wait. Propagation is quoted anywhere from a few minutes to 48 hours depending on who you ask, and there's no way to force it — the only honest way to check is asking DNS directly rather than trusting a timer:
dig NS miska.blog
;; ANSWER SECTION:
miska.blog. 3600 IN NS ns1.example-dns.net.
miska.blog. 3600 IN NS ns2.example-dns.net.
Once that query returns the new nameservers instead of the old ones, delegation is live, and every record from then on — CDN CNAMEs, ACME challenge records, the lot — gets managed in the new place. Until then, anything you configure on the new side is invisible to actual traffic, which is the failure mode worth designing your rollout around.