The fastest way in is by car. Metsovo sits beside the Egnatia Odos motorway (A2) about an hour east of Ioannina and an hour west of Kalambaka (for Meteora). The motorway tunnels straight through the Pindos massif; turn off at the Metsovo exit and climb the last few kilometres on the old road. From Thessaloniki the drive is around 2.5 hours; from Athens via Trikala it is about 5.
By bus, regular KTEL coaches run from Ioannina (about 1 hour) and from Trikala / Kalambaka (about 1.5 hours). There are also one or two daily services from Thessaloniki. The bus drops you in the centre, by the square.
There is no train. The nearest airport is Ioannina (small, mostly domestic flights from Athens), with Thessaloniki and Preveza the next nearest options.