Greyguard has been abandoned for two hundred years, and a section of the steps collapsed a century ago.
A Clash of Kings
Jeor Mormont, Lord Commander of the Night's Watch, plans to re-garrison the castle with men from the Shadow Tower, but on the advice of Qhorin Halfhand, they instead choose Stonedoor due to Greyguard's dire straits.
A Storm of Swords
A Dance with Dragons
Jon Snow, now Lord Commander, decides to re-garrison Greyguard with thirty men—ten from Castle Black, ten from the Shadow Tower and ten from King Stannis Baratheon—under the command of Janos Slynt. However, Janos refuses to follow Jon's orders, the second time publicly, which leads Jon to execute him at Castle Black.
The fort is in a sorry state, admittedly. You will restore it as best you can. Start by clearing back the forest. Steal stones from the structures that have collapsed to repair those still standing.