These books are specifically written to introduce LL.M. students and foreign lawyers to the U.S. legal system. Additional books on the U.S. legal system written for a variety of audiences can be found in the Law Library Reading Room at KF 385 - 387.
American Law in a Global Context by 
The American Legal System for Foreign Lawyers by 
Narrowing the Gap: Legal English for the New International Legal Practitioner by These books are specifically written to introduce LL.M. students and foreign lawyers to U.S. legal practice skills, such as legal reasoning and writing.
If you want more guidance specifically on U.S. legal writing, you can find books on legal writing written for a variety of audiences in the Law Library Reading Room KF 250s section.
U.S. Legal Reasoning, Writing, and Practice for International Lawyers by 
U. S. Legal Practice Skills for International Law Students by