Float Light Up
On the three nights prior to each of the float parades, some of the streets of downtown Kyoto are closed to vehicle traffic and the floats are lit up with lanterns. Around the streets you'll find all kinds of temporary stalls selling food and other items. The streets are crowded and many people wear yukata (summer kimono), it's an exciting time to be in Kyoto city.
The floats are lit up on the three nights prior to each parade. That is the evenings of July 14th, 15th, and 16th prior to the first parade on July 17th and the evenings of July 21st, 22nd, and 23rd prior to the second parade on July 24th. The night before each parade is called "Yoiyama", 2 nights before is called "Yoiyoiyama", and 3 nights before is called "Yoiyoiyoiyama".
It is possible on these evenings to actually go and see inside the floats, however getting a ticket to let you in is not an easy task. If you have a friend who's a Kyoto local they may be able to help you out. Otherwise just enjoy the close up view of the lit up floats from the ground.
Most of the floats are located on Shijo-dori or on side streets that run off Shijo-dori between Horikawa-dori (to the east) and Kawaramachi-dori (to the west). The best train stations to disembark from to see the light ups are Karasuma on the Hankyu Railway and Shijo-Karasuma on the subway Karasuma line. If you're using the Keihan Railway, then Gion-Shijo is the nearest stop to the light ups.
This photo was taken with a Nikon D700 camera and an AF Nikkor 24f/2.8D lens. Compared to the original image from the camera, in iPhoto I increased the definition, darkened the highlights and brightened the shadow areas.