There is no such thing as a stand along work permit application. You must either have an employment offer from an employer willing to sponsor you or be able to self-petition relying on your personal qualifications. There is also the option of starting your own company. Some of the most common visa involving a sponsoring employer are the H-1B, EB-2, EB-3 and L-1A- B. These visas require you to have an employment offer from a company in the United States who is willing to sponsor you through the immigration process.
The H-1B is what is commonly known as the visa lottery, where only a selected few applications get accepted for processing after millions of people apply. These visas are issued for 6 years or whatever your employment term may be. At the end of this period, you must change status to a different visa category or return to your country.
The EB-2 visa is designed for applicants with exceptional abilities or advanced degrees. This visa can be very complex and costly to achieve because one must go through the labor certification process, which involved publishing the job on various news sources and arguing that the intending immigrant is the only person qualified to fill the position. The EB-2 category does carve out an exception for professions that are of National Interest, waiving the labor certification requirement.
Similarly, the EB-3 is designed for applicants who qualify as professional workers with a minimum of a Bachelor’s degree, or other skilled or unskilled workers. This visa also involves the labor certification process.
The L-1A visa is designed for intracompany transferees in managements or executive positions who worked for a branch of the U.S. company abroad for at least a year. With similar requirements, the L-1B visa is for intracompany workers with specialized knowledge of the company procedures, services, products, etc.
There are many other types of temporary work visas that allow you to remain in the US for a specific period of time, including the TN visa for professional workers from Mexico and Canada, the O-1 visa for aliens of extraordinary abilities, the P-1 visa for internationally recognized entertainers and athletes, etc. There are also employment-based self-petitioning visas that grant permanent residence to its applicants without the need of a sponsoring employer, including the E-1 and E-2 visas for treaty traders and investors, the EB-5 investor program and the EB-1 extraordinary ability visa.