Ray Tomlinson created the first email program, for use with the ARPANET in the early 1970s (the first machine-to-machine electronic message apparently said something unpromising like "QWERTYUIOP").
Even with the ability to communicate to multiple users (until then, electronic mail had been limited to users of the same machine), this new 'email' would have been limited to people in the ARPANET directory.
Knowing that there were a limited amount of users to manage, what did Ray's inbox look like?
How did things like message-specific information like address/to/from display itself?
Computer mail was already in use for about a decade in late 1971 but was until that time constricted to users on the same machine, when Tomlinson combined a network file transfer program with those local mail tools (https://web.archive.org/web/20160205203944/http://openmap.bbn.com/~tomlinso/ray/firstemailframe.html) to create SNDMSG and made history by choosing the @-sign as separator between local part and hostname.
Now to the look of the Mails: According to the manual page the mail command in October 1972 (which should be the first version, which was able to send mails to a different host) just showed (or rather printed) the contents of the whole mailbox file. I can't find an exact description of what a mail looked like in that year but a year later RFC 561 gives an example looking pretty alike to modern mails:
From: White at SRI-ARC
Date: 24 JUL 1973 1527-PDT
Subject: Multi-Site Journal Meeting Announcement
NIC: 17996
At 10 AM Wednesday 25-JULY there will be a meeting
to discuss a Multi-Site Journal in the context of
the Utility. Y'all be here.
There's the header comprised of the meta information (like sender and date) and separated from the mail body by an empty line.
As the contents of the mails in Tomlinson's own words: "The early uses were not terribly different from the current uses: The exceptions are that there was only plain text in the messages and there was no SPAM." (https://web.archive.org/web/20160305210156fw_/http://openmap.bbn.com/~tomlinso/ray/firstemailside.html#6)