Employers can petition for workers to come or stay in the United States either permanently or temporarily. The employer can petition for the employee to start the process for the employee to get a green card or the employer can petition for the employee to come or stay in the United States on a temporary basis.
In order for employers to petition for workers, in many cases, they must first find out if there are any US workers that are qualified and available for the job. The employer files for a labor certification with the Department of Labor. Once the Department of Labor issues the Certification, the employer can petition for the employee with USCIS (formally INS).
If the person seeking their green card has spent any time in the United States illegally or entered the United States illegally, they may have other issues and should contact an immigration attorney to learn about their eligibility.