The activation is the same both in case of replacing an existing SIM card with an eSIM and in case of purchasing a new eSIM.
You can see the eSIM activation for iPhone in the video and pictures (the process is almost the same for other smartphones).
Below you can see an example of eSIM QR code:
The QR code is not an eSIM but a link to download it. That’s why you need a stable Internet connection to activate the eSIM with a QR code. If your smartphone doesn’t have a SIM card with mobile Internet, make sure to connect to an available Wi-Fi network.
If you’ve replaced a SIM card with an eSIM, the physical SIM card must be removed: it isn’t valid any longer. And if you want to move an active eSIM from one smartphone to another using the QR code, you need to delete it from the previous smartphone, so that it’ll be possible to activate the eSIM in the new smartphone. Don’t turn off the Internet until the downloading process and eSIM activation are completed.