The quickest way to get to Kyoto from Tokyo (513km) is by the Shinkansen Bullet Train, which is a marvel in engineering.
It takes 2 hours 40 mins to travel the 513km (318 miles) for around 13,500 each for a reserved seat. Pretty pricey, but worth it.
The seats are really comfy, with plenty of room. Book your seat on the right hand side of the train because at about the 41 minute mark you get to see Mount Fuji (if it's a good day) just behind you. Mind you, the day we travelled (at about 7am) the train was not very crowded at all.
This train is amazing, it travels at speeds up to 320 km/h (200 mph), placing them alongside the French TGV and German ICE as the second fastest trains in the world. It was much easier than heading to the airport in Kyoto and having to deal with airport check in and waiting around for departure/boarding/getting bags etc.