If you got engaged to a U.S. citizen and then entered the United States on a K-1 fiancé visa, and you are planning to make your permanent home in the U.S., it is best not to plan on leaving again soon. Ideally, you will not depart until you have already gotten married and submitted an application for U.S. residency (a green card). This article explains the details, namely that:
A fiancé visa is good for only one entry into the United States, so you can't later go out and come back using it.
If an emergency comes up before your marriage and you absolutely have to leave, try to make time to apply for a travel document ("Advance Parole"), using Form I-131 (available for free download on the USCIS website) first. You'll need to call its Contact Center first.
If you leave the U.S. without a travel document, the consulate might be able to revalidate your K-1 visa back in your home country, but it will take a hard look at your situation first. You could end up having to start over with a new fiancé visa petition.
There's also an exception ("automatic visa revalidation") for making short trips to the U.S.'s border countries, as described in, Can a Fiancé on a K-1 Visa Make a Quick Trip to Canada or Mexico?
In theory, once you have gotten married and turned in your application for adjustment of status (a green card) to U.S. Citizenship and Immigration Services (USCIS), any departure from the United States automatically cancels that application. USCIS will regard you as having abandoned your efforts. However, if you obtain special permission—called Advance Parole—the application will not be cancelled while you are away.
Obtaining Advance Parole is fairly easy when it's part of an adjustment application. Most applicants for adjustment of status simply include the form for it—Form I-131—along with their adjustment application, whether they plan on traveling or not. You need not pay any extra fee to include this application with your adjustment packet.
Of course, as a practical matter, you won't want to be out of the U.S. for too long while awaiting your biometrics appointment and later your in-person adjustment of status interview. Rescheduling can be difficult and lead to long delays.
If you, like many, find the immigration rules and procedures confusing, hiring an immigration attorney to analyze your situation, prepare the paperwork, and monitor your case until its approval can be well worth the cost.
Need a lawyer? Start here.