A pleasant 3 hours and 15-minute ride on the Shinkansen (Bullet-Train) takes you to Oishida Station. From there, most of the Ginzan Onsen Ryokan's have transport services although some of these are limited to a couple of times per day. If your train arrives at a time when they are not providing any pickup service, then you can get to your Onsen (hot-spring) by bus or taxi. With this in mind, try to schedule your arrival time to fit in with their pickup service as this will help your stay get off to a pleasant start.
Ginzan Onsen has recently been "discovered" by a great influx of foreign tourists, mainly from Taiwan and Thailand, so be sure to book early. If you don't, then you can always ask them to let you know if they have any cancellations.
We stayed at Notoya Ryokan, which was used for shooting many of the scenes in the TV series, 'Oshin'. That's why you'll find many of the visitors taking photos of the building.
Notoya Ryokan has the oldest onsen along the Onsen-gai (Onsen-Street). This consists of a small bath which is located down at the basement level and is available for private bathing. If you want to try it out, check to see if anyone has reserved it. If not, then you can try it. This bath is over a 100 years old. When the miners were digging for silver (thus the name Ginzan, i.e., Silver Mountain), they not only found silver, but also onsen water.
There are a number of onsens to choose from, and you can find plenty of information online. Many of them now speak English, at least enough to handle your reservations and requests. In addition to this, many of them also have English websites. With a little research, you'll soon be on your way.
If you go during the winter, be prepared for some snow! Yamagata typically gets over 9 meters of snow during the winter months.
Be sure to try some pickled watermelon. After trying this local speciality, you might even buy one of many mini pickled watermelons sold around town. Yamagata is well-known for watermelons; Japanese cherries, Yonezawa beef and Yamagata pork. You can even buy a Domannaka Beef Obento on the train for your lunch either on the way there or back.