On the following map, the Tokyo Bay Aqualine is displayed in blue, while the alternative journey by train+ferry is in red.

It took 31 years to study the possibility to build a road connection in the middle of the Tokyo Bay and build the Aqualine, which opened to traffic in December 1997 after 8 years of construction. The total cost reached... 1.44 trillion yens (11 billion dollars)!

from www.pref.chiba.jp/syozoku/b_soukei/keikaku/outline
The construction consists of two main sections. From the Ukishima access point, close to Kawasaki, a 9.6 km long tunnel (the longest tunnel for cars in the world) links to an artificial island, Umi-hotaru (海ほたる, English for "sea firefly"). From there, a long arched bridge of 4.4 km brings the cars to Kisarazu, in the Chiba prefecture. This bridge reached 41 meters, thus allowing 2000 ton boats to pass under it.

Views from that island :

This picture shows a schematic of the tunnel, which shows the 2 lanes where cars are driving. There is a second tunnel of the same size next to it for cars driving in the opposite direction. Each of the tunnels has a diameter of about 14 meters!
The crossing cost for a car of normal size is 3000 yens. The toll fee was higher at the inauguration, but it was later lowered since the traffic was much smaller than expected. The main concept behind this construction was to offer another way around Tokyo, thus lowering the number of cars crossing through the capital. But due to the hefthy fee, few people changed their habit. And this price is expected to increase to 4000 yens in 2008...
Crossing by bus
If you do not have a car, you can still enjoy crossing the bay via the Aqualine. Here is a list of some of the lines using this facility : www.keikyu-bus.co.jp/keikyu-bus/aqua.html
Links
www.pref.chiba.jp/syozoku/b_soukei/keikaku/outline/aqua-gaiyo-e.html : Detailed information on the Tokyo Bay Aqualine
www.takagi-ryo.ac/docs/id/140 : Some pictures taken during the construction of the Aqualine
web-japan.org/atlas/architecture/arc06.html : A couple of nice pictures of the bridge and the artificial island