To see if your book is a first edition, you need to look at the book's copyright page. You may see a series of numbers that looks like this:
10 9 8 7 6 5 4
The last number on the right tells you how often the book has been reprinted. In this example, the book is from the 4th print run. If the number on the right is a 1, then the book is a first edition from the first print run.
Some publishers, like Knopf, print "First Edition" (or "First American Edition" if the title was originally published abroad) on the copyright page, and do not use the number sequence as in the example above.