Checking the performance level of your iPhone, or any iOS device for that matter, isn't complicated. In fact, it doesn't even require a visit to the Apple Store.
Keep in mind, Apple isn't actually requiring your battery to fail its test to make you eligible for the $29 replacement. Checking your battery is more for peace of mind than anything else.
If after testing your battery you decide its time to replace it, follow Rick Broida's guide to make the process painless.
Apple Support app
This is by far the easiest way to check on your battery's health. Install the official Apple Support app and sign into your Apple ID if required.
Start a chat session with Apple Support, selecting the phone you want to have tested as the device in question. Once you're connected with a technician, inform him or her you want to know the status of your battery's health.
You will then be walked through the process, which requires going into Settings > Privacy > Analytics. A few seconds later, a report is sent to the representative.
My iPhone X battery passed with flying colors, as expected.
Naturally, the Genius Bar inside an Apple Store has all of the tools and resources required to run a diagnostics test on your phone's battery. You'll need to make an appointment through Apple's Support page and visit the store in person in order for the test to be conducted.
One reason to opt for a visit to the store to run this test is if you have questions beyond testing your battery.
If you want more info than a simple pass or fail, or don't feel like talking to Apple Support at all, you can install the third-party app Coconut Battery.
It's important to note, the app is not available in the App Store and installing apps outside of official channels is something you do at your own risk.
The free version of Coconut Battery requires the iOS device to be connected to your Mac via a USB cable.
After installing the app and granting it permission to run on your Mac, click on the iOS device tab, and look at the design capacity of your battery. Anything under 80-percent and you should take your phone in to have the battery replaced.