How do I set up a table of notes of phone conversations (text field) with dates (date field) that can later be searched by date?
With FileMaker open, go to the Help menu, Help->Product Documention and look at the getting started guide. It describes how to open files, add new tables and fields. It contains all the info you need and it's very easy to follow.
It would appear that you are describing the use of a portal to access/create/edit information. You would have a table of the people to whom you are having phone conversations--a table of contacts most likely and a related table of notes where you'd have a text field for notes, a date field that auto-enters the creation date and a "contact ID" field that links each such note record back to a specific contact in your table of contacts.
You can then use a number of techniques to search such a table of notes by date. The most straightforward interpretation of your request would be to set up a list view layout based on this notes table where you'd enter find mode and specify search criteria such as the date or a range of dates. The relationship between contacts and notes can be used with such a layout to include contact information from the contacts table along with the fields from the notes table.
There are also ways to filter and sort notes in the notes portal on your contacts layout by date if you need to see something like:
The most recent note for the current contact
All notes for the current contact on or after a specific date....
Retrieving data ...