Vienna to Hallstatt

Yes, the train station for Hallstatt is across the lake from the town. There is no train station in the town its self. You arrive at the Hallstatt train station and then take the ferry across the lake. There is nothing else there except the station and the ferry so you won't have any problem finding your way.

I don't believe there are any "direct" trains from Vienna to Hallstatt, as there's usually at least one change at Attnang-Puchheim. Check the bahn.de website for details. AFAIK the station in Hallstatt is not staffed, so you may want to purchase your ongoing rail tickets in Vienna as well. It may also be possible to buy tickets from the Conductor (not sure as I've never tried).

When you arrive at the small station in Hallstatt, you'll see the dock where you'll board Stefanie (or one of her "sister ships") for the short trip across the lake. The fare is about €2.40 PP each way, but may have changed.

Best to use www.oebb.at, the official website of the Austrian National Rail Service.

There is no direct service and the fastest routing will have you change trains at Attnang-Puchheim. The Hallstatt train station is across the lake from the town so the ferry shuttles the train passengers across.

Usual connection: Wien Westbahnhof direction Salzburg, get off at Attnang-Puchheim (not every train stops there) and change there for train to Hallstatt. There is a rail repair going right now so about 3 stations after A.T. you have to switch to bus to Bad Ischl and then continue by train to Hallstatt. Because of that there will be some delay. Important especially on the way back where connecting train from A.P. to Vienna will likely not wait.