Navigate to your group, then select Manage Members from the Management menu:

In the Actions menu, select Export | CSV Format:

CSV stands for Comma Separated Values and is one of the most common formats for import into spreadsheets and databases.

What happens next depends on your browser interface and the options you've set. In Firefox under Windows 10 I was offered an option of what to do with the file:

I selected Open with Excel. If you don't use Excel you can choose another spreadsheet application, or just save the file. If you save the file you can open it in an online spreadsheet such as Google Sheets.

Check to be sure you obtained the entire list. I've found that I often receive only the beginning of the file the first time I export, but trying again gives me the full list. Must be some kind of timing thing. People have reported the same problem in other browsers, such as Edge and Chrome.

Once you've obtained the entire CSV file and opened it in Excel you can adjust the width and formatting of the columns for legibility. The CSV file seems to be sorted by email address regardless of how you've sorted the list in the web interface.

The next step is optional, but if you're going to import the email addresses to another list service, or just copy/paste them into your email address book, you'll probably want to combine the Display Name (column A) with the email (column B) to form a more user-friendly email address. I've done this by making using a column over to the right from the import, and populating its first data row with this formula:

=IF(ISBLANK(A2),B2,CONCATENATE("""",A2,""" <",B2,">"))

Then copy that formula down the column, so that all of the email addresses are have their display names, if any. See the Excel documentation, but the short version is that ISBLANK(A2) is testing whether this member has a display name. If not then use just B2, otherwise concatenate a quote, A2, another quote, space, left angle-bracket, B2, and a closing right angle-bracket. In the example I've put yellow highlight on two pairs of quotes; this is a syntax trick in Excel, it is how you put a quote into a string.

Save your work as an Excel file to preserve the formula. Now you can select all the addresses in that column, copy, then paste into your list's new home.