Sometimes it's incredibly easy to identify a first edition, sometimes it requires specific knowledge (issue points).
What is a first edition?
A first edition is the first publication of a book to the public. Or at least that is the general consensus. 'To the public' is important as most books go through a number of stages before being published; manuscripts, uncorrected proof, advanced reader's copies. These, although collectible in their own right, are not generally seen as first editions. More often than not it is the first non-book club hardback edition that is collectible.
A lot of science fiction first hit the public sphere via publishers like ACE who published cheap, pulp paperbacks. These books, though still collectible, are rarely worth more than five or ten pounds. The hardbacks, even if published decades later, are usually worth much more. Similarly, collectors often dismiss book club editions, even where they're the first hardback edition.
As you move further back in time later printings and editions can still be highly collectible. Reprints of Darwin's 'Origin of Species' will raise a pretty penny. Certainly in the 19th and 18th century, collected works in multiple volumes can be highly prized. This is occasionally true with modern first editions too, books such as Fleming's 'Casino Royale' are highly valued in either the first or second state, or indeed any thereafter.
The Infamous Numberline
Recently over the last few decades publishers introduced a print line, called by various names such as a number line, impression list etc. The number line denotes the print run of a book and usually looks like this.
1 2 3 4 5 6 7 8 9 10
1 3 5 7 9 8 6 4 2
A B C D E F G H I
The lowest number denotes the print run. The two different types of numberline I think are due to the justification of the text block on the copyright page (ascending for left justified and ascending/descending for centrally justified). Every time a new print run is required the printer will remove the lowest number (or letter). Giving something like this:
3 4 5 6 7 8 9 10
5 7 9 8 6 4
G H I
Denoting a third, fourth and seventh printing respectively.Occasionally, if a book is very popular the numberline will be recreated from scratch starting one above the previous highest number:
11 12 13 14 15 16 17 18 19 20
Certain publishers, Random House and Villard I believe, have been known to use a number 2 to denote a first printing:
2 3 4 5 6 7 8 9
Another variation on the numberline is a single number on the copyright page, such as a 1 or a 2. These are usually on their own line. This is popular with the more recent books published by Voyager.
Other Methods of Identification
The numberline hasn't been around forever and some publishers don't use it. Cape, for example, simply state whether a book has been reprinted. During the middle of the last century, publishers would often just list the printings on the copyright page.
There are also a number of more obscure methods ranging from alphanumeric codes printed on certain pages to date stamps on the dust jacket.