
Enoshima has two good ways in: the direct, fast Odakyu line from Shinjuku, or — the more scenic option — the little Enoden train along the coast from Kamakura. If you're combining with Kamakura (recommended), the Enoden is half the fun.
If you're doing Kamakura and Enoshima together and riding the Enoden a lot, the Enoshima-Kamakura Freepass (or the Odakyu Enoshima 1-day pass) saves money once you hop a few times. For a single direct visit from Shinjuku, just reserve a Romancecar seat or tap an IC card.
Take the Odakyu line from Shinjuku to Katase-Enoshima (~70 min; the Romancecar is fastest). Or reach it scenically from Kamakura on the Enoden in about 25 minutes.
Yes — the Enoshima-Kamakura area passes bundle the trains and the Enoden, worth it if you hop between the two and ride the Enoden several times.