The ski slopes are located in different regions of the resort, so you may need to travel to reach some of them. In this regard, the Garmisch-Classic area is the most convenient and accessible, as you can easily reach it by bus. It's only a 15-minute ride, and you'll be on the snowy slopes. By the way, this bus service allows you to reach any desired location within the resort, as buses regularly travel in various directions. For tourists with a ski pass, the bus ride is free.
The second region, called Zugspitzbahn, even has its own train station. You can purchase a ticket for the train that runs along this route at the ticket offices of the main train station in the resort. You can find the full schedule of the train services on this page. If you want to reach the glacier, where you can ski year-round, you will need to transfer to the Gletscherbahn cable car.