1. google search my esri login
https://www.esri.com/en-us/my-esri-login
2. sign in with your arcgis online account, don't create arcgis.com public account. Because of misleading info in your my.esri invitation email send by esri, lots of people thought they should create a Esri.com public account to be able to connect to myesri. This is mis-understanding the email. The email actual means if you don't have arcgis online account, then you can create a public account. Since you already have arcgis online account, then don't create public account.
3. myesri invitation email
You already have arcgis online account, you can use that to sign in my.esri. You don't need to create a new public account. Lots of people don't realize this fact, they instead create another public account. This will result later, you can't access my.esri directly from your arcgis online page. I mean you will not be able to create direct connection between your arcgis online with your myesri. You can't switch between arcgis online and myesri by just click switch button on each side. Because you connect myesri to your another public account. You should connect myesri to your arcgis online account instead of another public account.
4. once you sign in myesri with your arcgis online account (do not create or use arcgis.com public account). Then you will see, you are not connect to any organization yet.
5. click the connect to my esri button in your invitation email. Now the button carry a 1 time use token to connect your whatever current login account on myesri to the organization that invite you.
5.1 once you click connect button in email, your myesri page will suddenly changed to show you the oragniaztion details home page
6. because I sign in myesri with my arcgis online account, now I can just click the link to switch to arcgis online without login. I also can switch back from arcgis online to myesri by just click myesri link. At this point, you create the connection between arcgis online and myesri with single login password. If you use arcgis.com public account previously you will not be able to create the connection switch between.
7. because I create arcgis online and myesri connection, this is my arcgis online account, I can just click my esri to switch back to myesri
8. I have both arcgis.com public account and arcgis online account connect to myesri
