Hello,
I'm here with a G1 visa . My mother who is not US citizen and not a green card holder, is planning to send me some money from her country, Italy. The gift is going to be used as a down payment to buy an apt. Is there any procedure I should follow with the IRS (I pay taxes in my foreign country as I work for an International organization in the US), or my mother in Italy? What is the amount max she can send me in the US?

In the U.S. the receiver of the gift does not pay at gift tax.

There are NO tax consequences for this gift.