Currently, there is no train service to Karpacz, however there are numerous trains (PKP) running from Wroclaw to Jelenia Góra daily (see a timetable: https://rozklad-pkp.pl/en). There, you can take a bus to Karpacz.
In details: direct trains to Jelenia Gora go frequently, every 1-2 hours. Then, in Jelenia, outside the train station, find bus no. 100 to Karpacz. It also goes every hour or so.
The town offers frequent services of private communication or PKS to Jelenia Góra. Time of travel is approx. 20-30 minutes. In addition, Karpacz has good connections with the urban areas in Poland (including Głogów, Legnica, Łódź, Wałbrzych, Warsaw, Wrocław and Zielona Góra).
There is a direct coach connection from Wroclaw to Karpacz by Flixbus https://www.flixbus.pl/
A distance from Wrocław to Karpacz is 120 km, which translates to a 2-hour drive on average. The route from Wroclaw requires you to leave the A4 highway at the Kostomłoty junction, and to take the no. 5 road to Strzegom and Jelenia Góra. In a place called Bolków the no. 5 road turns into the no. 3 road. At the outskirts of Jelenia Góra enter a ring road in the direction of Karpacz. You may also follow the road no.5 from Bolków. Head towards Kamienna Góra and Kowary, and then Ścięgny and Karpacz.
Wroclaw Airport (WRO) to Karpacz by bus
The journey time between Wroclaw Airport (WRO) and Karpacz is around 3h 54m and covers a distance of around 143 km. There is no direct bus connection on this route. All travelers must change at the Wroclaw station.