Direct trains run hourly from London King's Cross to Barnsley. Journey time: ~2 hours 30 minutes. One-way fare: ~£35 (advance booking can be cheaper).
Drive ~3 hours 30 minutes via the M1 motorway to Wakefield, then the A638 to Barnsley (~170 miles). Traffic around Sheffield/Leeds can add delays.
Direct National Express coaches take ~4 hours. One-way fare: ~£20. Less frequent than trains.
Verdict: The train is the easiest—frequent, direct, and city-center to city-center.