Stage 1 of 3: Interview the website owner and their development team. Ask them to tell you EVERYTHING they've changed on the site recently, even if it doesn't seem like it would be relevant. Very often clients and developers don't think that a certain site edit could possibly have affected their SEO traffic when it did.
Stage 2 of 3: Verify that there was an actual SEO issue. Sometimes people think their SEO traffic dropped when really it just returned to normal levels after an unusual spike, or GA tracking code got removed, or traffic dropped on ALL sources, not just SEO.
Stage 3 of 3: Find the cause. If you've verified that an SEO traffic drop really did occur, then it's time to find the cause. Easier said than done, of course, but I have more tips than this coming up.