The save system in The Bard's Tale Classic Trilogy dates back to the 1980s. There is no way to actually save your exact position and progress in these games in the more modern sense. However, you can save your characters and party, and continue playing with them later.
To save the game (i.e. your character progress) you need to go the Adventurer's Guild and select "Leave the game" from the menu. Then it asks you to "Press <RETURN> to save off all characters and end game play. Or press <ESC> to go back." Pressing the Return/Enter key at that point saves all your character progress.