I rented a car in Hokkaido last year. It came with an electronic tag somewhere on the windscreen, called an ETC card. The car rental and the tag rental were handled almost like two separate things I was renting. The car also came with GPS navigation which worked in English (be sure to request this in advance if you want it).
For the tag, I had the option of either paying a fixed amount in advance, or paying after I returned the car based on actual usage. Paying in advance gave a nice discount, but that turned out to be inflexible for my needs. Basically, I though it likely I would want to extend the car rental, but I couldn't extend the validity of the tag during the rental period.
One other thing, the highway tolls in Hokkaido were very expensive by European standards - I drove ~420 km on toll highways and the cost was a ~7,000 yen!
This site, from Nexco (the company that runs the toll system) will calculate tolls for you, though the route planning is only in Japanese http://global.c-nexco.co.jp/en/navi/