Device insurance is a contentious issue—it's expensive, and you probably won't ever need it. However, if you do destroy or lose a phone, you'd probably much rather pay an insurance deductible than buy a new device. If you like to play it safe, AT&T has open enrollment for insurance now through April 30th.
You usually need to add device insurance to your AT&T post-paid account no more than 30 days after getting a new device. For the next few weeks, AT&T will let anyone add a monthly insurance plan to their account (eligible devices only, of course). The cheapest options are $8 per month, but more expensive packages add things like priority support, cloud storage, and next day replacements.
You can sign up with your eligible device via the myAT&T app or on the AT&T website. The deductible is $50-200 depending on the type of device and how long you've gone without a claim.