You will not be able to apply in person for the visa in Madison, as there is no Chinese consulate general in in or around the city. The Chinese consulate general is the only authority that has jurisdiction to grant visas to an American wishing to visit China. You will need to go through the Chinese consulate general of Chicago, as its jurisdiction includes Wisconsin. You cannot go through any other consulate if you are a resident of Wisconsin.
Fill out the visa application form, which you can find on the Web site of the Chicago consulate. (Refer to resources for link to application). Type in the information, and print and sign the application.
Gather the required documents. Aside from the application form, you will need your U.S. passport (valid for at least 6 months,) one passport-size photo and the application fee of $130 in either a check or a money order. If you are a legal alien, a photocopy of your green card will also be necessary. (The additional requirements for work, student, journalist and residency visas are listed on the Web site of the consulate general).
Go in person to the consulate general of Chicago or hire a carrier service. You cannot send the application in the mail. There are many approved courier services you can pay to handle your application. They charge on average $30 to $60. Many offer expedited services as well. China Visa Service Center, Visa Master Service, Passport Plus and Passport Visa Express are some of the services. These companies are safe and much cheaper than flying to Chicago.
If you hired a carrier service, it will return your passport with visa once it has been approved. If you go in person, you will have to wait five work days, then collect it by using the the pick-up form that you were given on submission. Once you receive your passport with the visa, you are free to travel to China.