Day one: lock it and record it
Turn on the registrar transfer lock, confirm two-factor authentication on the account, and add the name to the company register with its purpose, owner and expiry. Set the renewal to multi-year and auto-renew from a company payment method.
Day two: decide what mail does
Before any MX record exists, decide whether mail to the new name is forwarded to the existing domain, rejected, or becomes the primary. Publish SPF, DKIM and DMARC for the new name whichever you choose, so nobody else can send as it. If the name will never send mail, publish v=spf1 -all, a null MX record (0 .), and v=DMARC1; p=reject;.
Days three to five: move web traffic
If the new name will be primary, replicate the DNS zone at your provider, lower the time-to-live on the old records a day in advance, then switch nameservers. Redirect the old domain to the new one with permanent 301 redirects, page for page, and update the canonical tags. If the new name is secondary, redirect it to the old one and stop.
Days six and seven: tell people
Update email signatures, letterhead, invoices, social profiles and the business listings that search engines read. Tell the bank, the accountants and the largest customers. Keep the old domain for as long as anyone might still be using it, which is longer than you think.
We walk every buyer through this on the day of release. It takes half an hour and it saves the month of confusion that follows a name going live before the redirects do.