What was put out at the last training I attended was that the player be within playing distance (about a foot or less from the ball) or touches the ball to be called. The wording: "is only penalized on becoming involved in active play by interfering with play by playing or touching a ball passed or touched by a team-mate..... The "Other Advice" beginning on page 192 further clarifies the different scenarios, Page 193 states "The assistant referee must raise the flag when the player touches the ball." Page 194 muddies things a little: "A player in an offside position may be penalized before playing or touching the ball, if, in the opinion of the referee, no other team-mate in an onside position has the opportunity to play the ball." This second one would be applicable if a lone player offside near midfield was chasing a long ball. The referee could make the call before the player reached the ball to avoid having the player run 30-50 yards.
LOTG 2016/2017 actually have some good diagrams and explanations for offside. They even have a section on teamwork, positioning,body language, communication and whistle beginning on Page 170 "Practical Guidelines for Match Officials."