Start with the Shetland Museum and Archives in Lerwick; the islands' flagship cultural institution, with collections spanning prehistoric artefacts, maritime history, textiles, photography and archives. It's where you'll find replicas of the Pictish silverware discovered at St Ninian's Isle, and where Shetland's story from the Neolithic to the present is told in full.
Beyond Lerwick, a network of local museums and heritage centres run by volunteers and community history groups covers everything from Shetland's crofting and fishing traditions to its role in the Second World War. Each one reflects a particular place and a particular community, the kind of local knowledge that doesn't make it into the big institutions.