There is a difference between 'edition' and 'impression'. The edition is the printing plates used, and the impression is the number of times books have been printed off those plates. Therefore a 'holy grail' is a first edition, first impression (or 1/1).
The edition can be determined by looking for the words 'first edition' or by the blurb on the inside of the book (it will say "first published..." and "this edition published..." if it says the latter it isn't a first edition, you only want to see the words "first edition published...").
To find the impression you need to look at the printer key (the sequence of numbers). The lowest number is the impression number, so your Harry Potter book with the numbers 20 19 is the 19th impression, but your Stephen King is a first impression.
If there is no printer key you can usually assume it is a 1/1. In the case of Bloomsbury (who publish the Potter books) all 1/1s are marked by the words 'first edition' and only later impressions have printer keys.