In the original Terminator film it was explained that the Terminator "begins systematically killing women named Sarah Connor, whose addresses he finds in the telephone directory" because all records were lost in the nuclear holocaust that followed in the rise of Skynet.
So, how did "Pops/Guardian" find the young Sarah Connor?
We don't know who sent "Pops", but we do know that Kyle Reese had a substantial advantage over the original Terminator because he knew which Sarah Connor was the correct one, having been briefed by John Connor himself.
On the assumption that someone with access to John (or Sarah Connor or Kate Brewster) was the one that sent "Pops", it would have also had the same advantage that Reese had.
Additionally, the reason why the original Terminator struggled was the volume of 'Sarah Connors' in the city. Since 'Pops' apparently tracked her down at home, he may well have had the details of her parents rather than just Sarah's name or he may have tracked her down by her name in school records, a technique that Cromartie uses in The Sarah Connor Chronicles
