The Asset Pack folder has another folder in it called "mods". You extract the ZIP there.

After that it should be as simple as going into the settings and dragging that into the "active" column. As far as I know this works on both Homestuck and Gio's versions of the UHC. Though I could be wrong, since I'm using an older version of Gio's UHC since the BCplayer mod broke over a year ago and Gio never fixed it (to be honest I have no idea what changes Homestuck even made to the thing).