How can you tell whether a hardback book is a first edition?
Are they valued more than those that are not first editions?

Check the date of the publication on the book, then double check it with information you find on the book - when it was written, first published, who published it. You can do that via a Google search or utilize your library and their staff, or take it to a bookdealer whose speciality is antique books and have it appraised. There are many factors to consider value, not just first edition status. For example, the popularity of the author is a factor. A first edition of a Hemingway novel will exceed the value of a first edition of a virtually unknown author. A second factor is the condition of the book - the bindings, paper, strains, rips, etc.

Yes, first editions are generally more valuable than second and third and so on. Remember that the value is multi-faceted. There is insurance value, historical value (in some cases), and the perceived value in a sale. The amount you come to after doing research may not be what the buyer is in agreement with.

Best of luck to you! Have fun!

Some will say "First Edition published...(date)"
Some simply "Published (year)"

More modern books have a number sequence on the copyright page that looks something like this:
1 3 5 7 9 10 8 6 4 2

The highest number (in this case 10) shows which edition it is.