In Hokkaidō distances can be deceiving. The website www.hyperdia.com has a schedule calculator that lists up-to-date options and prices for getting around.
Sapporo has flights to all major Hokkaidō locations, but rail, car or motorcycle are preferred. Trains run frequently on the trunk lines, but reaching remote locations (like Nemuro) involves infrequent trains and pricey buses. The foreigner-only Hokkaidō Rail Pass is also available: a four-day pass costs ¥14, 500.
Within cities, buses are convenient and usually cheap. Ask about a norihō dai (all day) pass if you’re going to use them a lot; it’s often a substantial discount.
If you have brought an International Driving Permit (you must get it from your home country prior to arrival in Japan), renting a car or motorcycle may save time. Local roads are often just as pretty as expressways and may yield unforeseen surprises. Car-rental rates vary, but if you walk in off the street expect to pay about ¥7000 per day, plus your first-born child for fuel.
For fans of greener ways to get around, Hokkaidō is a good place to tour by bike. Charida (bicycle riders) are a common sight on major roads. Rider houses are common and cheap.