1) If you haven't already, Download the Technic Launcher - You'll need it to download and play the mod pack.
2) Login with you Minecraft Cridentials - If your curious as to why, here's an article talking about it.
3) Download GTNH Modpack - Change to the Modpacks tab. In the Add Pack or Search bar, type in GT New Horizons. Pick the first result, not the Repack. (Shown in the image below)
4) Change to the Correct Version - After selecting GT New Horizons, click Modpack Options in the top right corner. Under Select Version, change from Recommended Version to A Specific Version:. The version that the server runs is GT New Horizons v188.8.131.52. Double check this because it's VERY important
Version: GT New Horizons v184.108.40.206
5) Press the Download Button - At this point, you can officialy download the modpack. Hit the download button in the bottom right corner.
6) Increase your RAM - GTNH Requires at least 4GB. Hit the Launcher Options in the top right corner. Change to the Java Settings tab. Under Minecraft Java Version, make sure that you pick a 64-Bit version. After that, under Memory change to at least 4 GB. The correct settings are shown below.
7) You're All Done! - After the modpack finished downloading, you can play!