1. By car Zermatt is one of the car free cities; you can reach by car as far as till Täsch. There you can park your car and take the shuttle train to the city. Alternatively you can go either by taxi or by regular train.
2. By train There is a train station in Zermatt which you can reach directly.
3. By plane Zurich is the closest airport and from there you can take a direct train towards Zermatt. The trip takes about 3,5 hours.