SPF
Add include:spf.privateemail.com to your existing SPF record. Do not create a second record: two SPF records mean neither works, and that is the most common mistake in this whole area.
A complete record with Namecheap Private Email alone looks like v=spf1 include:spf.privateemail.com ~all. If you use other sending tools, their includes go in the same record.
DKIM
Found in Private Email dashboard, or the Namecheap domain's Advanced DNS if the domain is with them.
Namecheap publishes the DKIM record automatically when the domain and the mailbox are both with them. If the domain is elsewhere, you add it by hand.
Namecheap Private Email publishes keys under the selector default, which is what an external check looks for.
DMARC
DMARC is the same regardless of provider, because it is your instruction rather than theirs. Start at v=DMARC1; p=none; rua=mailto:you@yourdomain.com, read the reports for a few weeks, authorise everything legitimate, and only then tighten. The DMARC guide covers the order in detail, and the order is what stops you blocking your own invoices.
Worth knowing with Namecheap Private Email
The automatic setup only applies when domain and mail sit in the same account. Moving the domain away later leaves the mail records behind, and this is a frequent cause of mail breaking weeks after a registrar transfer.
Check it afterwards
Publishing the records is not the same as them working. Verify from outside: whether SPF passes, whether a DKIM signature is actually present, and how many lookups your SPF now performs. The free mail check answers all three in plain language.