Hunting for 1st pressings

Some can be identified by cover details. There are may be notes only belonging to the first edition. Clear example is Magical Mystery Tour where later editions had many faces blanked out because public figures did not want to be displayed on the record cover. Same story with Rolling Stones "Some Girls". Another clear example is Led Zeppelin "In Through The Out Door" with bunch of different cover variations.
Many shaded dog releases would mention on the cover "previously released as (on different serial number)". 
There are also labels that only did re-issues such as Arkiv re-issued Deutsche Gramophone
Apparently there are and there aren't simple ways to ID 1st pressings.

It really depends on the record- there are some 'known' first pressings that have a history that has been documented. Are you looking at rock/pop stuff or classical/jazz? Very different markets with different knowledge bases.....

First pressings are often if not always best sounding and worth pursuing.

+1 on last comment by inna. Worth the effort IMO.

As an example. I have Pangaea by Miles Davis on Japanese vinyl, three pressings - original pro, original regular and same year reissue.
There is no doubt that the original regular is better sounding than reissue, and the pro is better still and not by little.
Another interesting example comparing original American and original Japanese. Bitches Brew by Miles Davis. They sound somewhat different - the American is a little more raw and edgy and Japanese is quieter and more refined, both are quite dynamic. I listen to both American and Japanese, though Japanese more often.
And the last example. Inner Mounting Flame by Mahavishnu Orchestra. Original Japanese and Japanese first reissue. They sound different, the original is a little more dynamic and the reissue is more refined and a bit laidback. Both great, I listen to the original.