Tokyo's Major Streets
sign displaying the town address (courtesy Wikipedia)
town block indicator plate (courtesy Wikipedia)
In years past very few streets in Japan had names other than some of the major thoroughfares. These days it's possible to find more streets with names, but other than the major ones, most people won't know where "such and such" a street is located.
Some use the word "kaido" in their name. The "Kaido" generally follow the old roads used by warlords of days gone by for their annual, required, trip to Tokyo. In some areas newer, wider roads have been built that closely parallel the old kaido. These are usually called "shin kaido" (new kaido).
Some of the more common, and better known, roads are Koshu Kaido (Route 20); Sakurada Dori (dori means street, so one shouldn't say Sakurada Dori Street); Ome Kaido; Inokashira Dori; Roppongi Dori; Aoyama Dori, and a few more.
However, don't look for a US style address like 1234 Aoyama Dori. Such addresses don't exist. The address will still be listed in ward, "chome" (district) then "gou" (block) then "ban" (house / building number) format (example, Shibuya Ku [ward], 5 chome, 22 gou, 4 ban; written as 5-22-4). The building numbers are not in an easy to follow order. For example, in the USA, one expects to find building / house numbers in a progressive address system such as 1234, 1236, 1238, etc. In Japan the building number usually signifies the order in which that building or house was built in that particular chome. Think of it as a big puzzle - it often is - where you have a whole puzzle that represents Tokyo.
The easiest way to find an address is to use an online map, but when that's not available stop by a kohban (police box). They always have maps of the area and most police can direct you to the area you want to go. Once you're i the right block it may take a bit of walking around though to find the house/building number. If you're asking someone their address ask for landmarks too, which often make it easier to find a particular building.