Machynlleth is on the Cambrian Line, one of Wales's most scenic rail routes. Direct trains run from Shrewsbury (1.5 hours), Aberystwyth (30 minutes), and Birmingham (2.5 hours). From Cardiff, change at Shrewsbury; from London Paddington, change at Birmingham New Street. The station is a few minutes' walk from the town centre.
By road, Machynlleth is on the A489/A487 junction. From the A470 (the main north-south route through mid-Wales), turn west at Cemmaes Road. From the coast road at Aberystwyth, it's 20 miles east. Parking is available in the town centre car parks off the main street.
There is no direct road to Machynlleth from the M4 or M54 that avoids the mountain roads of mid-Wales — any approach from England involves winding A-roads through the Cambrian Mountains. The rail option is often faster and considerably more scenic.