Most washers and dryers are similar to those in the west, except they are usually smaller. The dryer's lint trap is a plate shaped screen in the back of the drum. Be sure it's cleared of lint. Depending on your clothes, it usually takes at least two runs through the dryer, and if it's plugged with lint it will take longer.
There is almost always a laundry detergent vending machine in the laundry room.
One place we stayed at, Hotel Area One in Kagoshima, has a washing machine and dryer in one. You don't have to add soap either, as it's fed in from a tube. The strange thing about this washer is that it locks your clothes in until it's done.
If your place of lodging doesn't have a washing machine, an interesting thing to try is a local coin laundry. You can get a taxi ride from your hotel or ryokan. It might be best to take your clothes in a trash bag, rather than your suitcase, so your hosts don't think you're skipping out on the bill. Your hosts may also be able to recommend a near-by laundry. Sometimes coin laundries are located in covered malls and you can go shopping if it's not too late. You may also meet interesting people. While your clothes are in dryer you can study Japanese by reading the signs the signs on the walls. Try this one:
If you do wash at night and your place of lodging has a curfew, make sure you get back before the front desk closes.
Here is some useful vocabulary from Jim Breen's dictionary.
洗濯石鹸 【せんたくせっけん】Laundry soap
洗濯機 【せんたくき】Washing machine
コインランドリー (n) laundromat; laundrette
洗濯ばさみ 【せんたくばさみ】Clothes Pin
１０００円札をくずしていただけませんか。 Could you change a Y1,000 note?
I especially like the word くずす - literally crush or destroy. Used here to mean "make change".
One way to stretch out the time between having to do laundry is to do it in your room. This is one reason to pay a little more for a room with a bathroom (some minshiku and ryokan have community facilities). Often the bathroom will have a clothesline in the tub/shower. You may want to bring your own line and some small plastic clothes pins or buy them at a 100 yen store. We travel with little packets of Woolite and wash clothes in the sink. This is why we wear synthetics almost exclusively. Although wool and cotton are comfortable, they take forever to dry, especially if the weather is humid.