On Windows there are no permissions to grant, and setup skips this step.
On a Mac, Dolfinspeak asks for three permissions when you first set it up:
Microphone, so it can record your voice and anyone in the room with you.
Accessibility, so it can paste finished results into the app you're using.
System audio, so a recording can include sound playing on your computer, like the other people on a call.
Grant them
Setup needs Microphone and Accessibility before you can continue. Accessibility opens System Settings instead of showing a prompt. If you later turn a permission off, turn it back on here:
Open System Settings → Privacy & Security.
Under Microphone, turn on Dolfinspeak.
Under Accessibility, turn on Dolfinspeak.
For system audio, open Screen & System Audio Recording (Screen Recording on older versions of macOS) and turn on Dolfinspeak.
On a Mac, you can also check Accessibility from Settings → Permissions in Dolfinspeak, which has a Request access button.
If a change doesn't seem to take effect, quit and reopen Dolfinspeak.
If recordings work but nothing is pasted into your app, Accessibility is the usual cause. See Recording isn't working.