I'm renting a car soon in Japan and am planning to travel on the expressways. What's the best way to pay tolls?
There are two options.
The easy way is cash, which is (at time of writing) still accepted by every toll plaza on every Japanese expressway: just collect a chit on entry and pay when you leave.
But if you're driving longer distances or on multiple days, you'll want to look into getting set up for ETC (electronic toll collection, but called "ETC" even in Japanese). This requires both a reader mounted on the dashboard, which is standard equipment in Japanese rental cars, and an ETC card, which is used to bill you. Getting your own card is a bit of a hassle if you're not a resident, but fortunately most (but not all) rental agencies participate in a scheme that lets you rent one for only around ¥300 for two weeks. It's worth calling ahead to check if one will be available though; if not, you can use Tocoo's postal rental service.
Convenience aside, while standard toll fees for ETC are exactly the same as paying in cash, having an ETC card also lets you take advantage of a plethora of discount schemes for weekends, late nights, etc: http://www.japanetccard.com/discounts
Particularly useful are the tourist-only regional Expressway Pass schemes, where you can pay flat fees of as little as ¥500/day to use them. http://www.go-etc.jp/english/expressway/index.html
These are quite a deal if you're driving longer distances, as the regular toll is around ¥25/kilometer, meaning (say) Sapporo-Obihiro, a distance of under 200km, would cost you over ¥5000 otherwise.