Jury selection for the trial began in Sioux Falls on Thursday, where Mr Jones was arrested and charged following a bar fight last December.
Prosecutors accuse Mr Jones of hitting Juan Trevino-Barrera three times.
The X-Men star, 44, received hospital treatment for cuts to his face he suffered during the altercation.
Mr Jones, who was in court on Thursday, is charged with simple assault, an offence that carries a maximum punishment of one year in jail and a $1,000 (£657) fine.
Mr Trevino-Barrera claims he was playing pool in the city's Wiley's Tavern when Mr Jones asked if he could play.
The actor, whose films include Lock, Stock and Two Smoking Barrels, and Snatch, is alleged to have taken offence when he was asked if he was "that guy from X-Men".
Mr Trevino-Barrera claims he was punched in the head by Mr Jones following a scuffle in which one of his friends struck the former Wimbledon player with a beer glass.
Jesse Bickett, of Montrose, South Dakota, was arrested in December for his part in the brawl.
The trial is expected to last one day.
In 2003 Mr Jones was given 80 hours community service for "air rage" offences on a Virgin Atlantic flight.