The most common way is to apply the extension via Config. Example:
# File: mysite/_config/config.yml
Member:
extensions:
- MyMemberExtension
The extensions config variable is of type "array", so you can add multiple extensions like this:
# File: mysite/_config/config.yml
Member:
extensions:
- MyMemberExtension
- MyOtherMemberExtension
If you wrote the class that is to be extended, you can define the extension(s) as static variable:
<?php
class MyClass extends DataObject
{
private static $extensions = ['MyCustomExtension'];
}