How can I change the battery safely?

Although my esteemed colleague @jayeff has given you the 100% correct answer to your question, there are a few caveats to replacing the battery on your phone that you may not be aware of.

First off, once you replace the battery, you will then start receiving a pop-up warning when you turn on your phone that the battery may not be genuine - even if it is a genuine Apple Battery. That's because Apple has started pairing the battery's BMS, or Battery Management System - the small circuit board mounted on the battery - to your phone's logic board. It uses a proprietary encryption algorithm that only Apple has access to, so no one else can pair the battery to the phone other than Apple.

In addition, you will lose access to the battery health information, which is extremely useful in helping determine when to replace a worn-out battery. Obviously this won't be of any importance for at least a couple of years down the road, but Apple does disable it when it gets the non-genuine warning.

Of course, the aftermarket industry tends to be quite creative when it comes to repairs, and they have worked out a way around these issues. As you might guess, it ends up making a simple battery replacement into a semi-complicated surgical operation.

The first thing that has to happen is that you have to keep the original BMS in order to avoid the warning. That means you have to basically disassemble the battery and remove the BMS circuit from the old battery. Then you have to buy a replacement battery cell, one that comes without the BMS ($10 USD), and spot weld ($40) the original BMS onto it.

That gets you past the non-genuine warning and the missing health information. Unfortunately, keeping the old BMS means keeping the old battery health information, consisting of the health percentage number (0-100%) and the cycle count, or number of times it's been charged and discharged. On phones prior to the iPhone 11, you could simply plug the battery into a device programmer ($85) and reprogram those numbers, but once again Apple has decided to make life miserable for those who want to do their own repairs. They've changed the way the health information is stored such that it can no longer be accessed using a device programmer.

Once again the aftermarket industry has come up with a workaround, this time in the form of a tiny little circuit board called a tag-on flex cable ($7) that plugs in between the battery and the logic board. This circuit allows you to access the health information and reprogram it with a device programmer. Note that in the process of looking one up for this answer I found one that says it does not require reprogramming, which I take to mean that it comes pre-programmed with the health percentage and cycle count set to 100% and zero, respectively. That would be good, as it would save you the $85 for buying a device programmer.

Anyway, the tag-on flex is installed permanently in the phone along with the battery and can be reused should the battery need replacing again; however you would need a device programmer this time to reset the health settings.

So there you go; thanks to Apple's refuse-the-right-to-repair policy, a simple process of open the phone, replace the battery and close the phone becomes major surgery and complicated ordering of parts and equipment.

To sum up here are your choices:

1. Pay Apple to replace your battery; everything's hunky-dory.
2. Use the Self Repair service to do the job yourself; of course you still have to buy the battery from Apple and rent their equipment to do the job as well as register your phone with them so you can use their "calibration tool" to pair the new battery to your phone. Slightly less expensive, but still far from what you can do it yourself for; however, no warnings and health information works.
3. Replace the battery yourself and live with the pop-up warnings for a week or so until they stop by themselves. You will, however, have a permanent warning badge on your Settings icon and the warning will show up under the Battery part of the Settings app. And, of course, you will no longer be able to view the health information.
4. Buy anywhere from $60 to $150 worth of parts and tools in order to get around Apple's deliberate obstacles to self repair, surgically remove the BMS, spot weld it to a new cell and add in a tag-on flex. As I said, a lot of work for what should have been a simple battery replacement thanks to Apple and their repair-antagonistic approach.

And that's all I got to say about that.