There are shagloads of items on the internet about naturalizing or changing from a green-card holder to a citizen. Just google any of those keywords or phrases and you will get literally hundreds of millions of hits. Here is a starter
Citizenship is a unique bond that unites people around civic ideals and a belief in the rights and freedoms guaranteed by the U.S. Constitution.
www.uscis.gov
Her Japanese citizenship isn't an issue as far as her obtaining US citizenship goes. The US no longer cares (much) if you are a dual citizen. So she can apply for naturalization regardless of her Japanese passport. There are no pitfalls, other than some financial complications that arise from dual nationality (tax issues, social security benefits) but rest assured your friend is not the only one who has faced these issues.
The only potential problem with nationality is on the Japanese side. Japanese citizens are not supposed to have dual citizenship, as you know, and if you obtain another citizenship you are
supposed to make a declaration to the Japanese authorities telling them which one you intend to abandon. If you go to the Japanese authorities with the intention of abandoning Japanese citizenship, they may take you through the process right then and there and ask you to forfeit your Japanese passport. (It may actually be more complicated than that, I don't really know). If you go to the Japanese embassy with the intention of forfeiting your foreign citizenship, they may ask you to sign an affidavit saying that you abandon your other citizenship, and that you are henceforth only a citizen of Japan. (Note, Japan cannot cancel your foreign citizenship, they can only compel or coerce you to abandon it).
BUT all of this is what you are
supposed to do. In reality, many people simply keep their 2nd citizenship quiet, and the Japanese authorities never query them about it. Japan is on a demographic downward slope, so Japan doesn't want a further exodus of potential citizens. Japan also needs to compete with the rest of the world in retaining talent, and aggressive persecution of dual citizens would harm Japan's image as a work/life destination. There seems to be a tacit acceptance of dual citizenship, even thought the law books still say that only one citizenship is recognized. (I bet Japan will even reverse course in the future, and will eventually allow dual citizenship).