Fingerprint identification was suggested in the 1880s and used within the courts in the eartly 1900s. Before that, witness evidence, particularly of identification was seen as the best evidence. Credibility was at a different level then and a God fearing society nearly all took the oath in court. They were more in fear of crossing religious oath in those days.
I am really glad that we have fingerprint, DNA and other forensic technology, as witness testimony is often inaccurate, even when given with the best of intentions, such is the rationalizing nature of the human brain.
Mark is more the expert on this, so I will leave that to him.
From my limited knowledge, it was drawings of suspects from witnesses, witness statements and more obvious evidence (such as finding the murder weapon, etc.) – so science is moving this area of Policing a lot forwards.
I believe that retinal scans are more accurate than fingerprint identification as there have been several cases of mistaken identity of suspects from fingerprints (i.e. someone was physically in another country so couldnt have been at the crime scene, even though the fingerprint evidence had identified them there!).