You've got the basic idea right:  basic major & minor chords consist of the 1st, 3rd & 5th of their parent scale.  The E minor scale is:

E (1st) - F# (2nd) - G (minor 3rd) - A (4th) - B (5th) - C (minor 6th) - D (minor 7th)

So an E minor chord is the 1st, minor 3rd and 5th of the E minor scale.  Those notes are:

1st - E, minor 3rd - G, 5th - B

This is typically done by playing

|--0--(E)--|
|--0--(B)--|
|--0--(G)--|
|--2--(E)--|
|--2--(B)--|
|--0--(E)--|

But you can simplify it down to just those 3 notes, because that's all you need for a chord.

|--0--(E)--|
|--0--(B)--|
|--0--(G)--|
|----------|
|----------|
|----------|

This tutorial covers the basics of chord theory.

https://www.guitartricks.com/tutorial/148

Hope that helps!