In "The Lottery," how long had the people been using the box?

Nobody knows exactly how long the current box has been in use.  The only specific detail that the reader is told about the age of the box is that it has been in use for a long time.  The box has been in use since before Old Man Warner was born.  That is a significant amount of time, because Old Man Warner is the oldest man in the entire town.  

. . . and...

Nobody knows exactly how long the current box has been in use.  The only specific detail that the reader is told about the age of the box is that it has been in use for a long time.  The box has been in use since before Old Man Warner was born.  That is a significant amount of time, because Old Man Warner is the oldest man in the entire town.  

. . . and the black box now resting on the stool had been put into use even before Old Man Warner, the oldest man in town, was born.

Of course being the oldest man in a town that practices a raffle to stone people to death might mean Old Man Warner isn't that terribly old.  But in this case, Old Man Warner is indeed an old man.  While Old Man Warner's exact age isn't specifically stated, the reader is told that he is participating in his 77th lottery.  That means the box is at least 78 years old.

A bit later in that same paragraph, Jackson provides further evidence that the box is indeed quite old and well used.  The text explains that the wood is splintered badly and faded in odd locations, which is evidence of age and dry rot.  

The black box grew shabbier each year: by now it was no longer completely black but splintered badly along one side to show the original wood color, and in some places faded or stained.