SharePoint - Access methods for external users

General info

When you share a SharePoint item (site, page, folder or document) with an external user (e.g. an author), you share it with their email address. The user receives an email with a link to the share item.

The external user has to verify that the email is theirs, to make sure it's not just a link someone got a hold of.

There are three ways to verify that they have the email address:

They have their email address registered with Microsoft via their company because they use Microsoft services (called "School or Work account")
They have signed up with their email address at Microsoft.com and have created a password (called a personal account)
They confirm they have the email by getting a onetime code sent to their email address

When they click a link to a share SharePoint item the email address is embedded in the link and will be used for access to the item. The email address will be checked against Microsoft and they will get an option to enter the password or prompted to enter a code.

Best practice when sharing with externals

Have the external user register their email as an account with Microsoft before you share any link with them. This is how:
Go to https://www.microsoft.com, click "Sign in" at the upper right corner
Click to create a new account and follow the registration. If the email is already signed up as an account they will be notified on the screen and can instead reset the password if they have forgotten it
When the external person has successfully logged into the Microsoft page, you share the SharePoint site/folder/document with them to the email they are signed up with