Home Assistant and ESPHome How-to Series 1: Step 1- Overview and Parts
Home Assistant and ESPHome How-to Series 1: Step 2 – ESPHome Add-on
Home Assistant and ESPHome How-to Series 1: Step 3 – Make a Simple Media Speaker
Home Assistant and ESPHome How-to Series 1: Step 4 – Centrally Controlled Thermostat
This is the next one in the ESPHome How-to Series 1. Hope this makes sense...
Here I am going to talk about installing ESPHome Add-on into Home Assistant. Before I go on, I wanted to make sure it is clear that this option works if you are running a HA supervisor. So, if you are not sure that is where you need to start. If you are using a Home Assistant device then it has a supervisor. A quick way to tell is to look for the Add On option under Settings
If Add-ons 
is there then you have Supervisor option and can continue to install ESPHome Add On in Home Assistant.
So, click on the next step is simple. Click, 
button and find ESPHome add-on as shown below.
In there are currently three options. Use ESPHome one for released version of ESPHome. The other options are for non-released versions. They may not be as stable as the released version. However, there may be a reason you would want to use them so decide which one you would like to use. Below, I have added some great sources that expand on this post. Enjoy!!!
Other Sources
https://esphome.io/guides/getting_started_hassio.html