The power of Google's search engine makes finding archived emails fast and easy. The big search field that runs across Gmail's top border works for most things but sometimes the number of emails returned is just too large. You can add additional search terms or the name of the sender but using some clever search operators, you can also narrow your search significantly and precisely. You can search in the Subject line only, for example, or combine that with the date range, or exclude all messages with attachments.
To access the search detail options, click the arrow at the right end of the big search field at the top.
To search for a phrase, use quotation marks. Example: "school board meeting" otherwise Google sees them as individual words but not necessarily in that order or together.
To search for an email that has the words supplies and art but not necessarily together you would enter supplies AND art. The search operator (in this case, and) must be in all caps. That's how Google knows they're separate words. The same goes for OR. To search for an email that has the words supply or supplies, you would type supplies OR supply.
You will usually want to change your search scope from "All Mail" to Mail & Spam & Trash to cover all your bases.
There are a multitude of search operators that you can use if you're really adventurous and want to try them out. https://support.google.com/mail/answer/7190?hl=en
Once you use the search details a few times you'll realize how powerful it can be for finding mails that may be buried deep (without scrolling!) and you'll get better at it each time.
TIP: If you don't get the search results you were looking for, sometimes entering less search criteria is better.