See also the official documentation:
Help Center > Members Manual > Working with group messages > Searching for messages in the archive

Here's help on using the Groups.io search engine.

Word-based search of the message archive:

To get there, log on to the site, find your group, click on the Messages button on the menu bar at left, then click on the Search button at the top of the resulting page.

A dialog box will pop up to accept your query. The engine uses the standard Boolean operators AND, OR and NOT. You can also search for quoted phrases.

Examples:

• telescope AND observatory -- find all messages containing both of the words "telescope" and "observatory"
• telescope OR observatory -- find messages containing either "telescope" or "observatory" (may contain both)
• telescope AND NOT observatory -- messages containing "telescope" that do not contain "observatory"
• "my observatory" OR NOT telescope -- messages that contain either the quoted phrase or do not contain the word "telescope"

These operators must be in ALL CAPS. If you use lower case, the engine will assume you meant to find messages containing these actual words. Also, if you forget to insert any Boolean operator, the system defaults to AND. Thus, "telescope and not observatory" is equivalent to "telescope AND and AND not AND observatory." 

Only whole words are matched -- entering "telescope" in the engine will not find the word "telescopes" in a message. However, the * wild card does work, thus searching on telescop* will find "telescope", "telescopes", telescoping", etc. 

The search encompasses only the Subject and Body of the messages, not the From or To addresses. If you need to find all posts by a subscriber, this is accessible via the "More" menu, found at the bottom right of any of their messages.

Search by date:  

While we're at it, try clicking on the little button to the right of the search button (it's supposed to look like a funnel). This will display an additional pull-down menu labeled "Any Time" (which is the default). Click on that pull-down to further filter your search hits by posting date. When you are given results to a search, a Tools button appears to provide some additional filtering/display options.

[Last Updated: 14FEB2019 (Ref: https://beta.groups.io/g/main/message/19838)]

Search by hashtag:

You can fine-tune your keyword search of the message archive by adding a hashtag - such as premium #database to your search string.

You can also select #hashtags from the menu on the left on your homepage. You can click on the number of posts with that hashtag. A good example is #changelog.