There's nothing I can find explaining what Lupin did exactly during his transformations, but we can infer he most likely would disappear, take himself off to a remote location, and transform into a werewolf far away from other people.
We know he didn't have access to the Wolfsbane Potion until he started teaching at Hogwarts:
Remus had no chance to sample it [the Wolfsbane Potion] without admitting what he was and so he continued his lonely, itinerant existence.
...He was only persuaded to accept when Dumbledore explained that there would be a limitless supply of Wolfsbane Potion
Wizarding World - Remus Lupin
He did have jobs before working at Hogwarts, but never kept them for very long. The following quote tells us that Remus, who is currently living hand to mouth, is more willing to stop working and leave without any further explanation after only a month or two than feed himself.
Remus now lived a hand-to-mouth existence, taking jobs that were far below his level of ability, always knowing that he would have to leave them before his pattern of growing sick once a month at the full moon was noticed by his workmates.
Ibid. (emphasis mine)
Additionally, even though the above passage is more about the stigma of being a werewolf in the Harry Potter Universe, Lupin's worry about having his monthly "habit" being recognised and leaving before being noticed is amplified when we read about his fear of biting someone else.
It had always been Remus’s worst fear that he would kill while out of his right mind.