In order to use WSJT-X, an amateur radio operator (ham), or a short wave listener (SWL), needs the following:
1. A frequency stable radio and an antenna (the frequency range for both depends on the band);
2. a sound card interface in order to pass the received audio to a computer;
3. a copy of WSJT-X, available here (for Microsoft Windows, Linux or Macintosh);
4. an accurate computer clock.
The antenna depends on the band you wish to use, as well as how you would like to use WSJT-X. You may want to use 160 meters, which generally requires large wire antennas, or the microwave bands with a dish to bounce signals off the moon. WSJT-X is popular on the HF amateur bands, but is also used on VHF for EME, as well as meteor scatter, rain scatter, airplane scatter, or even to bounce signals off the Internation Space Station. Perhaps you will have a unique idea for its use.
Note that the program is designed for weak signals. Weak signals does not mean low power. On 20 meters many hams use low power (10 watts or less), but for EME, some hams use 1500 watts of output. As with all other amateur communications, the idea is to use the least amount of power necessary. If you can work the world with milliwatts, that's great. If it takes 1500 watts on 6 meters to have an EME QSO, that is also fine.
Many computers using Microsoft Windows are not very time accurate. If your PC's clock is off by just 5 seconds and you are attempting to make a QSO via meteor scatter using 15 second intervals, then you are missing one third of the receive and transmit time. Likewise your chances of having a successful QSO using 5 second intervals, then that QSO will be very unlikely to complete.
Computer time accurancy is much more important in the utilization of the FT8 mode.
There are numerous third party time clients available on the Internet for Microsoft Windows (Google is your friend).