In Gmail, click the settings gear in the top right, and then click settings.
Then, click "Accounts and Import."
In "Accounts and Import" you'll see a few sections, one of them labelled "Send mail as," click the "Add another email address" link there.
Type whatever you want in the Name field (It will be shown on messages you send) and enter your email address in the Email address field.
Check the "Treat as an alias" box and go on to the next step
The SMTP Server will be filled in for you, now enter the full email address in "Username" (Ex: joe@periodic.xyz") and enter the password for the email, located on your account page into the password field.
Finally, click "Add Account" and click the link in the verification email Gmail will send you.
For non-Gmail clients, use the SMTP server mail.periodic.xyz (TLS, port 587), with the username equal to the email you're using, and the password located in your account page

In order to keep costs low, emails are not stored on the mail server, and instead mailed to an email address you already own.
This has benefits in that you do not need to trust that I don't store and spy on your emails, once they're forwarded to you my server no longer has them.
Another obvious benefit is that instead of requiring a fee per GB of storage, you only have to pay for emails.
Finally, emails are forwarded because it's convienient to not have to log into each email individually, you can read emails sent to any email address you own all from one primary email address and client.