Hello, my wife is a Korean citizen while I am a U.S. citizen. We got married a couple months ago and have filed for a form I-765 so she could try to get a job here to be able to pay for her citizenship forms. They sent in a mail today and have asked that we register for a I-485 form to be able to complete the process for I-765. After looking at a couple of sites we found that she would need a k-3 visa before getting an I-485. She came here through her student visa but it should expire soon. What would be the best next step for her to get a job to support us financially?

You can't just get an EAD because you want to get a job. Only certain classes of people can apply for EADs. One such class is Adjustment of Status (I-485) applicants. You can apply for an EAD for free at the same time as, or after, you apply for Adjustment of Status.

For her to immigrate, what she needs to do is apply for Adjustment of Status (I-485), the process of getting a green card inside the U.S. No, she does not have to K-3 visa or anything; a visa is for someone to get into the U.S. and she is already inside the U.S. As long as she entered the U.S. legally, and is your spouse, she can apply for Adjustment of Status. You will file a petition (I-130) together with her I-485, and there will be lots of supporting documents needed.