If a permanent citizen of United States wants to marry a foreigner, then the fiancée may require the fiancée visa to enter United States.
K1 visa generally has short waiting period as compared to those of immigration visas based on marriages. By filling form I-765, you can apply for the work permit and also engage in employment. You can also apply for the citizenship of your children if they are under 18 years of age, after you get the K1 visa.
For filing up the petition for marriage visa, K1 visa, fiancée visa etc., you must fulfill some of the requirements. First of all you and your fiancée both should be eligible for the marriage under the laws of the country. Your fiancée should enter the country within six months from the date of petition and after the entry, you should get married within 90 days, otherwise your partner will have to leave the country. Before filing the marriage visa, you must have met your fiancée at least once in last two years.
There are some documents that you must have before filing the petition. The documents include valid passport, copy of your birth certificate, copy of your divorce papers (if applicable), death certificates, medical documents proving that you are fit to enter the country etc. You should also have evidence that your fiancée is able to support you financially.