Travellers from Glasgow can take the train from Glasgow Central station (lower level) direct to Lanark. Travellers from Edinburgh can take a train to Motherwell (don't change at Holytown, which has no station facilities) and change there for a train to Lanark.
Irvine's Coaches operates an hourly coach service [240X] to Glasgow from Monday to Friday between 0600 hours and 1800 hours. There is also a reduced Saturday service. There's no direct coach or bus from Edinburgh, but you can make local connections by taking the bus to [wiki=6bda4c16ffba6999365b4c48419dc79f]Biggar[/wiki], from where you can catch a bus to Lanark bus station. There are also regular buses both to and from the nearby town of Carluke.
Lanark lies at the junctions of the A70, A72 and A73 roads, all of which were major trunk roads before the building of the motorways. New Lanark is signposted on brown tourist signs from the M8 and M74 motorways.