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Hello. Both ways are possible.
For teachers:
1) Go to My Students>All students, then select a student or students you want to move;
2) Select the action "Remove from all groups", and click "Apply the selected items";
3) Select the student(s) again;
4) Select the action "Add to groups", click "Apply the selected items",
5) Choose the group and click "Apply."
For students:
1) Log in with your username and password;
2) Click "Add to group";
3) Enter the Group code (given by the teacher);
4) Click "Submit".
Hope it helps.