+12 C (53 F) is common at nights even in the hottest month of the year (August), so be sure to take at least a cardigan, if not something that would keep you warmer.
Vangölü Ekspresi ("Lake Van Express") departs from Istanbul’s Asian station (Haydarpaşa) twice a week on Mondays and Fridays at 10:55PM and arrives in Tatvan station after a 40-hr journey, on Wednesdays and Sundays at 2:17PM. This train also calls at a number of cities and towns across Asian Turkey, including Eskişehir, Ankara, Kayseri, Sivas, Malatya, and Elazığ among others. Inter Rail pass is accepted in this train. See Turkish railway authority’s website  for detailed information.
There is also another train from Elazığ, passing Muş on the way, which operate at least once weekly. It arrives at Tatvan at Tuesday evenings.
Train station is in the upper part of the town (northwest of downtown), about 20 minutes walk away from the town centre. It's off the main highway to Bitlis, but its entrance is not immediately visible from the road because of some buildings and trees inbetween—you may have to ask around.
The station lies at the end of a spur line—the main line normally heads straight to the train ferry harbour. All passenger trains to the area do make the de-tour and call at the station, though.
Train ferries connect Tatvan with Van, a rather large city located on the eastern shore of Lake Van. These ferries accept pedestrian passengers whether they have a connecting train ticket or not. It takes four hours to cross the lake.
Ferries crossing the lake depart from north of the town centre at ~05:00 and ~13:00 (5 TL)
Town's small otogar (bus station) is located on the highway to Bitlis, north of downtown, about half an hour's worth of walk from town centre, and not very far from the train station. Dolmuşes are also available to the centre. However, most inter-city bus companies have offices in town centre, too. In fact, most otogar offices are open only during day hours, with most companies prefering to use central offices during the night, which are far more convenient during the day hours, too.
Tatvan itself is not renowned for its historical or natural gems as it is rather a bleak town of mostly new, concrete development. It mainly serves travellers as a jumping off point to sights further afield.
A handful of hotels are located in the town centre along, or just off, the main street (near the post office). Most are clearly sign posted.
Camping by the lakes on Mt Nemrut is also a (free) option. Although the amount of litter can be a bit off putting.
The telephone code of Tatvan is 434 (+90 434 when calling from out of Turkey).
There are numerous internet cafes dotted along the main street in the town centre (some more modern than others) costing 1.50 or 2 TL/hour. There is one just upstairs from office of Van Gölü Seyahat bus company in town centre, open till late at night and very convenient if you're looking into spending your time until your departure.
Trains — trains to Istanbul depart twice weekly - only on Tuesdays and Thursdays at 7:10AM. If you happen to miss the train of the day, nearest station is in Batman - which has trains to Istanbul the following day (i.e. on Mondays, Wednesdays, and Fridays). Trains also depart from Batman in the morning (around 9AM). Van Gölü Seyahat has a night bus (at midnight) from Tatvan to Batman which costs 15 TL/person/one-way, arriving at Batman's otogar around 4:30AM. Walking otogar to train station take about one to one-and-a-half hour in Batman. Alternatively, you can take buses to Istanbul directly from Tatvan, but they cost more than double (70 TL/person/one-way) of what the train costs (about 30 TL/person/one-way).