As with other Mac OS X applications, you can type smart quotes using the appropriate key sequences. For example, on a US keyboard they are:
“ Option-
” Option-Shift-
‘ Option-]
’ Option-Shift-]
You can also Control-click in a text view and choose Substitutions > Smart Quotes to enable automatic insertion of smart/curly quotes when you type dumb/straight ones. EagleFiler currently does not remember this setting between launches, however.