Is it the one you downloaded through steam I think there is a small difference between the original one and the new ones being released if that was not patched up already through steam already but whatever haven't played a half-life mod in ages!
If its anything like modding half-life 2 there should be a file like source mod or steam mod just dump everything in there. Also there should be a readme file that came with the download that gives you instructions on how to install it.
edit:
http://halflife2.filefront.com/file/HalfLi...ey_Hunger;18269As I expected I looked up on filefront the game does not work with the game of the year version and it seems like you just dumb everything in the file directory of half life. I never played the mod but here is what the link said to do
3) Now start HalfLife normally.
4) From the main menu, click on "Custom game". You will see
now a list of all the mods available on your computer. Select
"They Hunger" and click on "Activate". (If you don't see an
option "Custom game" then you have to update your version
of Halflife!)
5) Select "Done" to return to the main HalfLife menu. The
"They Hunger" logo should appear on the screen.
6) Now start a new game and select your skill level. You are
now playing They Hunger episode 1!
7) If you wish to only play They Hunger episode 3, then you
must first start a new game and select your skill level.
After this, press ESC and click on option "They Hunger 3".