How do I email my professor about assigning me to a group?
Keep it simple:


  Dear Prof. X,
  
  I'm Hannah Y (ID n. 12345), an international student in your class
  XYZ. Since I don't know anyone in the class, could you please assign 
  me to one of the project groups?
  
  Thank you,
  
  Hannah


I have international students in my classes and such emails are not uncommon. The important thing is to provide all the pieces of information needed to identify you and the course (professors usually have several).