I am currently a student in US. Last 1 year my grandmother purchased land in my name. I work part time here. I am not married. Am I liable to pay the Zakah on that land? Is Zakah compulsory on me now when I am working part time. If so, how much should I be paying and to whom? Please give me a detailed answer so that I do not have any more doubts in the future.

Praise be to Allah, the Lord of the Worlds; and blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
Everyone who owns a house or a piece of a land not for business but to live in owes no Zakah on those things. The Zakah is compulsory only when one uses them for business after the passing of a complete Lunar year on possessing them, and provided their value reaches the Nisab (the minimum of one's holding liable to Zakah) which is 85 grams of pure gold. Then one has to pay 2.5 percent of the value of all articles of merchandise. The companion of the Prophet Samurah Bin Jundub said: "The Prophet used to command us to pay Sadaqaat from [the goods] we had for sale".
As for the recipients of the Zakah they are only eight categories as Allah mentioned in this verse: {As-Sadaqât (here it means Zakât) are only for the Fuqarâ (poor), and Al-Masâkin (the poor) and those employed to collect (the funds); and to attract the hearts of those who have been inclined (towards Islâm); and to free the captives; and for those in debt; and for Allâh's Cause (i.e. for Mujâhidûn - those fighting in the holy wars), and for the wayfarer (a traveller who is cut off from everything); a duty imposed by Allâh. And Allâh is All-Knower, All-Wise.} [9: 60].
Allah knows best.