By train: The fastest way in is by JR Yokosuka Line from Tokyo Station (one hour) and Yokohama (25 minutes). The JR Kamakura-Enoshima Free Kippu (about ¥1,200 from Yokohama, about ¥2.000 from Tokyo) gets you a round trip from Tokyo to Kamakura (local trains only) plus unlimited use of Enoden and Shonan Monorail lines.
A cheaper alternative is to take the private Odakyu line from Shinjuku to Fujisawa, then change onto the rattling old Enoden, half-train/half-streetcar line that terminates in Kamakura. The longer (about 90 minute) travel time is compensated for by views of Enoshima island and the Shonan coast. The Enoshima-Kamakura Free Pass (about ¥1,500) will get you a roundtrip from Shinjuku and unlimited use of the Enoden line for one day.
Kamakura is just a little too big to cover on foot, but a network of buses radiates out from the train station. Kotokuin and Hasedera can also be reached by taking the Enoden line three stops out to Hase station.
Nevertheless, for the energetic ones, there is a nice hike starting from the Tokeiji and ending near the Kotokuin. You will walk, with some climbing, through forest. The hike also passes through Zeniarai Benten Shrine, if you are curious about the money washing ceremony. The hike takes about 3 hours, if you also stop and visit the temples along the way. Even in Summer, the shade on the path manages to keep the temperature bearable (you still are in Japan in Summer, anyway!). If you are on a day-trip, doing the hike of course limits a bit the chances of visiting some of the less reachable temples.