Tobias Leung ’s answer is terribly irresponsible, let me give you the genuine answer.
Here’re the steps to mail letter to President Xi. (Source: New China Agency)
Step 1 Mail your letter to Zhongnanhai Fuyou Street Branch Post Office 中南海府右街邮政支局.
This post office is the only one which provides postal service to Zhongnanhai.
Step 2 Transfer to the State Bureau for Letters and Calls 国家信访局
Zhongnanhai Fuyou Street Branch Post Office will handle letters from populace to the State Bureau for Letters and Calls. Sorting room might do the first sort, and distributes different type of letters to 8 different offices. These 8 offices might sort letters again, and register the ones that comply with the Regulations on Petitions in the Form of Letters and Visits online, then the senders could check progress online. Moreover, the offices also have to notify the senders by mail, or phone.
Step 3 Reach to the President!
As we all know, President can’t handle all the letters. Officers will only present the list of those valuable letters, or in brief forms, to the President, weekly. For those VIL (very important letter), the original letter will be transferred to the General Office 中央办公厅, and the General Office will put the letter on President’s desk.
Who had gotten reply from President Xi himself? (source: People.com)
(※This is not the full roster, just part that had been publicly reported※)
4/17/2008, to Tan Jianyi, and Zhu Chenhan, 6 grades elementary school students from Peiling, Chongqing.
5/2008, to 30 CPC’s rural branches’ secretaries from Zhongwei City, Ningxia Muslim Autonomous Region.
7/2008, to villagers from Liangjiahe Village, Yanchuan County, Yan’an City, Shaanxi Province.
3/2009, to elderly from Community Association in Macao SAR.
9/2009, to Principal Yang Zhenyu of Liening (Lenin) School in Huachi County, Gansu Province.
11/2009, to Wang Boxiang, retired secretary of the Shouguang County Committee of the CPC, Shandong Province.
2010, to retired members of Dachen Island Reclamation Team, Taizhou City, Zhejiang Province.
5/12/2010, to Bo Junli, 6 grades students from Yingge, Taibai County, Shaanxi Province.
8/2010, to students from 8–1 section of Minzhu (Democracy) Junior High School in Xujing, Qingpu, Shanghai.
6/2011, to Wen Jianming, secretary of Chengnan Town Committee of the CPC, Yingshan County, Szechuan Province.
7/2011, to Community Committee of the CPC from Xiaoyingxiang Community, Hangzhou City, Zhejiang Province.
10/31/2011, to Lv Wenkai, elementary school students from Mengyin County, Shandong Province.
5/2/2013, to Archaeological PhD students from Peking University.
10/2013, to entire students from the Affiliated High School of the Central University for Nationalities.
12/2013, to Benyu Voluntary Service from Huazhong Agricultural University.
2014, to Chinese students in Germany.
5/18/2014, to 55 entrepreneurs from Fujian Province.
5/2014, to 16 elementary school students from Tasmania State, Australia.
