The first step is usually an assessment against current requirements: egress window size, minimum ceiling height, fire separation from the main unit and, in most cases, a separate entrance. An older basement built before current code frequently needs structural changes before the application can even be submitted as complete.
Homes where the space was already close to code, adequate ceiling height and a window that only needs enlarging, move through inspection and permit review noticeably faster than homes needing new framing or an engineered structural change, so the honest answer is measured in weeks to a few months rather than a fixed timeline.
A home inspection beforehand, typically $400 to $600, is a reasonable way to scope how far your specific basement is from that starting point. Get your hand-reviewed valuation from Joel Dyck.