So we needed this and it's in a confusing as heck position, so hope it helps you.
Well all the disclosure I legally need to do is "This is a Microsoft-sponsored post.", but well, more details. I'm part of the Microsoft Student Partner program, which provides me access to tons of info on Azure and free access to Azure, so this post might be biased.
Now, to actual content
Login here. Click on "More Services".
Search for "Subscriptions", click on it, and then the subscription you want.
Click on Access control (IAM).
Click on Add, select a role.
Enter a mail address for the user, tick the box, hit OK. They'll get a mail.