K-3 is for a spouse of a U.S. citizen residing abroad.K-4 is for the unmarried child of someone eligible to be a K-3.

If a U.S. Citizen gets married abroad, you can either be

Interviewed for a green card abroad or come to the U.S. with K-3 and be interviewed in the U.S. The faster procedure is to bring the spouse to the U.S. with K-3

First you have got married.

Second, file form I-130 and obtain a receipt.

Third, obtain approval of form I-129F attaching the I-130 receipt to the application along with supporting documents.The Immigration has a special office in Chicago for this application.

Fourth, obtain the visa and come to the U.S.

Fifth, apply for a green card.