How do we apply for a Corporation

It depends on the State in which you want to incorporate. Usually, Articles of Incorporation are filed with the Secretary of State or official charged with this function. You will also need to follow the corporate formalities under the State Corporation Act, as well as obtain a Federal Employer Identification Number and if appllicable, file for subchapter S status with the Internal Revenue Service. See a lawyer. The ramifications of screwing this up far outweight the nominal cost of getting it set up correctly.

DISCLAIMER- THIS IS NOT INTENDED TO AND DOES NOT CONSTITUTE LEGAL ADVICE AND DOES NOT ESTABLISH AN ATTORNEY-CLIENT RELATIONSHIP.
Thomas Martin’s answer gives you links on how to form an Arizona corporation. However, from your question, it seems you might be referring to the need for a Mexican corporation to own land in Mexico. I am not licensed to practice law in Mexico, and this answer is not intended to give you legal advice on Mexican law. I do, however, often work with Mexican lawyers and Mexican notarios públicos (notaries public) to assist our non-Mexican clients (usually U.S. and Canadian based clients) to purchase, sell and develop property in Mexico. This answer is intended to give you some general information, and is based on the information provided to me by Mexican lawyers. I have worked with Mexican lawyers in helping numerous people acquire property in Mexico. Sometimes this involves forming a Mexican corporation. Often, it involves forming a Mexican bank trust that will own the property. Sometimes, it involves forming an Arizona corporation or limited liability company (“LLC”) that will own the Mexican corporation or will be the beneficiary of the Mexican bank trust. The option that is best for you depends on your particular situation and preferences. If you would like, I’d be glad to discuss your specific situation with you or refer you to a Mexican lawyer.
First, you should understand that no corporation is required in order to own land in Mexico, though you might want to own the land through a corporation for various reasons. Non-Mexicans cannot acquire direct title to property in the “Restricted Zone” (i.e., within the area 100 kilometers from the Mexican border, 50 kilometers from the beach, and all of Baja). Perhaps this restriction is the reason you are saying you need a corporation to legally own the land. There are two legal ways for non-Mexicans to enjoy the benefits of “ownership” of property in the “Restricted Zone.”
The first is that non-Mexicans can acquire full rights to use, rent and sell property in the Restricted Zone by having title to the property transferred to a Mexican bank trust of which the buyer is beneficiary. The trust can be created for an initial term of up to 50 years, which is subject to renewal for an additional 50 years upon the request of the beneficiary. If the property is already in a Mexican bank trust, the buyer can have the beneficiary rights assigned to the buyer.
The second (for “non-residential” properties only) is through a Mexican company (which could be a corporation or limited liability company). The Mexican company may be wholly or partially owned by non-Mexicans, provided the permit and registration requirements for foreign ownership are met. However, it is important to understand that non-Mexicans can legally avoid the Mexican bank trust requirement by owning through a Mexican company only if the property qualifies as “non-residential” property. Depending on the circumstances, “non-residential” property can include houses, condos and apartments that are owned and rented as a business and such properties that are bought, developed and sold as a business. A Mexican lawyer or notary public can advise you whether the property would qualify as “non-residential” and allow you to own it through a Mexican company, rather than a Mexican bank trust (assuming you are a non-Mexican and the property is in the Restricted Zone).
If the property is not in the Restricted Zone, then non-Mexicans and Mexicans can own direct title to the property, and Mexicans can own direct title to property throughout Mexico. Under these circumstances, no Mexican company or bank trust is required.
However, even if a business entity is not a legal requirement, it may be advisable to own the property through a business entity, rather than owning it under your own name. Owning the property through a business entity may serve to protect you from personal liability (e