You don't need any particular subjects in your undergraduate degree to get into law school, however classes involving logic and writing are generally considered useful. Also, people with master's degrees in subjects such as science and engineering are often in demand to do intellectual property, health law, and other such work.
You will also need to complete the LSAT.
To get into Yale, you'll need a straight A average from a top school, a LSAT mark in at least the 98th percentile, plus excellent references and extracurricular involvement.
After you complete law school you will then need to pass the Bar Exams. If you want to work in Canada, etc, then you will also need to "article" at a law firm for a year after completing the above.