If you are currently awaiting approval of a K-1 fiancé(e) visa, it may be some time before you can legally work in the United States. Before that happens, you will have to enter the U.S. on your K-1 visa, and then either:
We'll discuss both possibilities below.
A work permit, also called an employment authorization document or EAD, is a small plastic photo identity card that shows that USCIS has approved you to work in the United States. You will need to show it to your employer on your first day of work. You can also use it to obtain a U.S. Social Security Number, which employers require in order to pay your employment-related taxes.
A K-1 visa allow you to enter the U.S. and remain for 90 days in order to get married and, if you wish, apply to adjust status. If you want to work during those 90 days, one option is for you to apply to USCIS right away for employment authorization, on Form I-765. You will need to pay a fee ($380 as of 2016).
The catch, however, is that by the time you have submitted the form to USCIS and it has processed it and made a decision, the 90 days might have passed. As of 2016, USCIS's typical processing time for an I-765 was, coincidentally enough, 90 days. That may change someday, but it's been fairly typical for several years.
No matter how long USCIS takes to approve an EAD, it will give it an expiration date of the end of your 90-day permitted stay on your K-1 visa (the exact date of which is shown on your I-94 Arrival/Departure Record). Given these realities, it would probably make more sense to wait and use the option described next, of simply getting married and applying for a work permit along with your adjustment of status application.
As soon as you have entered the U.S. on your K-1 visa, the clock starts ticking. You have 90 days within which to get married, obtain the official government certification of your marriage (which can take days or weeks), and prepare the mountain of paperwork required for your adjustment of status application (which you'll submit to USCIS by mail). The sooner you get this done, the sooner you'll get your approval for U.S. residence.
One of the forms you'll want to include in your adjustment of status packet is Form I-765, for a work permit. Good news: You don't have to pay an added fee for it if it's included in this packet. Once USCIS processes it, you'll receive an EAD with an expiration date that's likely to be a year long, to cover the period while you await your green card interview at a USCIS office.
Some people decide to work illegally while they are awaiting clearance to work with a pending K-1 visa. Working illegally is a violation of your visa status -- and if you're not in valid visa status, you're not eligible to adjust status and get a green card. Consult an immigration attorney for details.