Firstly we have do electronic configuration of that element having atomic number Z
See in which shell last electron lies .If the last electron goes to second shell, then the element is in 2nd period.
Now, see the outer most electron ,also it is called valence electron, if the element having valence electron 3, then it will lie in 3rd group.
Hence the position will be, 2nd period, 3rd group.
Hope now you understand the actual concept of finding the position.