I arrived by train in Gotha. Gotha is served by IC and regional trains. The railway station is quite small. There is a small bakery shop though. For drinks etc. there is a well selected small shop by the tram terminus. And behind the tram terminus you will find a supermarket.
If you just need a single journey within Germany search the DB website for "Dauerspezial". If you plan to travel for several days within Germany and are living in Europe but outside Germany then you may be better off with the Interrail One Country pass.
The Thueringer Waldbahn is actually a tramway that takes you from Gotha railway station to the Kurort of Tabarz in the Thuringa forest. It's line number 4 and the journey takes about one hour
I bought a "Touristenticket" for Euro 7.30 which allows you to use all the trams in Gotha and the Waldbahn for one calendar day. Attached are some discount vouchers for a few attractions along the line.
I bought my ticket at the hotel reception but you may also buy it in the tourist office or probably also from the tram driver. Don't forget to validate it in a little machine by the tram door.
The journey to Tabarz takes you through Gotha and then out into the countryside. Later you will enter some forests.
On the second photo you will see a map of the line.
There are several tram lines in Gotha. You can buy a ticket from the driver. A few lines start at the railway station. Some tram lines circle more or less around the old town.
You could easily walk from the railway station to the old town. But if you prefer to take a tram, you get off at the 5th stop for the tourist office in the old town.
On the third photo you find a line map.