When a book person raves about having a First Edition of something, they (assuming they know what they're talking about) are actually saying two things: that the book is a first edition, and that it's a first printing as well. A book that is a first edition as well as being a first printing is called a True First.
If you look at the copyright page of practically any book put out by a major publisher, you should see two things related to this discussion - there is (usually, though not always) a block of text reading FIRST EDITION towards the top of the page, and there should be a list of numbers towards the bottom of the page. This number series is the print run information. All first printings are first editions, but not all first editions are first printings.
These numbers can come in various forms that vary from publisher to publisher. For instance, these...
9 8 7 6 5 4 3 2 1
1 2 3 4 5 6 7 8 9
1 3 5 7 9 8 6 4 2
2 4 6 8 9 7 5 3 1
are all print run numbers from true firsts (assuming we're not dealing with a book club edition
. More on that in a minute). These...
4 5 6 7 8 9
9 8 7 6
33 32 31 30 29
. You're looking for that precious number 1. If it doesn't appear anywhere in the series, it's not a true first. If the book has the last example as print run
information and doesn't specifically say it's a first edition on the copyright page
it's pretty well set that the book is worthless from a collector
There are three other things to keep in mind:
Firstly: Book club editions obey a completely different set of rules: most of them have different ISBNs and different printing standards than their original editions - the paper is cheaper, the binding shoddy, etc. Since they're technically different books the print run numbers start all over again, creating the impression that the book you're holding in your hands is worth way more than it actually is - book club editions are usually almost completely worthless. There are exceptions to this rule - some have extremely interesting dust jackets that can raise their value considerably, but that's not at all common. Certain other things (extra marks on the copyright pages, altered dust jackets, the lack of a price or barcode etc.) help to differentiate the two printings.
Secondly: Country of initial publication matters a great deal. Apart from textual differences (idiomatic expressions, etc.), cover art, introductions and the like, a book isn't technically a first edition if it was published previously in another country - those two versions are treated as separate books with separate ISBNs and separate values. In general, British first editions (for instance) are worth a good deal more money in the states, partially because the print runs are smaller and partially because British editions of books are quite difficult to get over here.
Thirdly: the print run numbers of books published by Random House always start with 2 instead of 1. Why this is, I have no idea, but it's good to keep in mind when hunting.