Whether you have your own transport or use public transport Minehead Tourist Information Centre Can advise you of the best way to arrive. Just contact the team on 01643 702624 or email firstname.lastname@example.org
And while you're here, why not enjoy some car-free time?
There is a regular bus service linking Minehead to Taunton rail station which travels via Watchet. There is a service west along the coast to Porlock Weir and a seasonal service further west to Lynmouth. See the TravelineSW website for details.
Why not arrive in style on the West Somerset Railway, which runs from Bishops Lydeard to Minehead? Or take a trip on the train whilst you are here making the most of the views along the coast and Quantock Hills..