How do you know when an LP is a first or early pressing?

There are two distinct inquiries here- one is how to determine if a record is truly a first pressing, which not only involves an examination of deadwax nomenclature, but label, including logo, sometimes the packaging, and what country of issue as well. There’s a lot of minutae in this but the info is out there on various websites for different labels, bands and genres and Discogs is a good place to start.
The second area of inquiry is connecting this information with sound quality and that’s more difficult in some ways because it depends on listening evaluations and comparisons. You can do this yourself if you have the time, money and ability to source multiple issues. You can rely on anecdotal comments from others who have done the comparisons. For classic rock, the older threads on the Hoffman board are good, at least those that are in depth and not simply comments stating that their copy "sounds good." The Better Records/Tom Port thing is a whole other subject that is fairly controversial and I’m not going to wade into that.
In some cases, with rare jazz records, there aren’t numerous pressings- often just an original run and sometimes a second pressing, followed years later by reissues, often with a big question mark about source- needle drop, digitized, etc.
I have found, in the classic rock area, that the sonic differences do not necessarily correspond to any rational relationship with when the record was issued-- oddball reissues by the label itself that sound better than first pressings, differences in EQ and tonal balance that may favor a later (but still early) issue over a later one. There are also "known" hot pressings of some of these records. I think it is very hard to generalize and the knowledge that has developed over the years, after the fact, by collectors and sound hounds (two different species) is often siloed by band, particular album, or label. There are also shortcuts in some instances that can save you money where the metal parts from an early desirable pressing show up on a later, much cheaper period reissue. The quality of the vinyl used at the time is also a factor, so there are many variables. I have found that I have accumulated many copies of records I like but aren’t the best recordings or pressings and the end result is comparing different sets of compromises, occasionally resulting in no one "best" sounding copy, but shadings of difference with various strengths and weaknesses.
This is, as EBM said, something that you develop over the years, with accumulated knowledge based on first hand experience having gone through a lot of records. I have done purges over the years to get rid of thousands of records that didn’t make the cut and got sidelined-- to the point where I needed to make space and saw little need to keep the lesser copies. That said, I still have some albums where I probably have a dozen different copies. This was not the result of just a few years, but decades of buying.

ELP’s first album is one of the last pink labels before Island started using the pink rim in the UK. By the time of the pink rim, Island was pressing and distributing through EMI and the deadwax reflects EMI nomenclature. Previously, Island worked with Polygram, which used a different type of code in the dead wax. (Every once in a while you’ll find an old pink rim that used the metal parts from an earlier era-- I have a Free Tons of Sobs that bears the Polygram nomenclature even though by the time of that reissue its manufacture should have been EMI). The early pink labels are yet again different, some pressing at Orlake, with different nomenclature--Those tend to be the "bullseye" pink labels. I suppose one might find an Orlake on a slightly later pink label- after bullseye, there was the ’blocked I" in black, then the white unblocked "i," which was the last variation. These would be shown in a book like Yuri Grishin’s (if you are referring to his series on famous British labels). At the time this stuff was manufactured, it was a commodity and the average user wasn't necessarily focused on pressing plants. Even the record company executives wouldn't have paid much attention to pressing plant issues, except for business reasons; the relationship between deadwax and sonics was not even on their radar. Much of this information was unlocked by collectors years after the fact. Island was sold to Polygram and eventually merged into the Universal empire. Who knows what documentation exists for manufacture- it wasn't necessary paperwork that would have carried over through various company transfers. 
And that’s just the pressing plant! Island also used a variety of mastering engineers including Sterling in the U.S. and George "Porky" Peckham, whose work (he often did the remasters in the period) was bombastic.
I generally prefer the earliest pressings on Island for sonics, e.g. Orlake over Polygram and Polygram over EMI- this is reflected in the prices as well-- The EMIs tend to sound a little hotter and brighter, the Orlakes, though a little noisier, are richer sounding. Some of the early pink labels fetch real money these days. Chris Blackwell and his crew were way ahead of the pack in signing very forward looking artists and wound up with a roster of talent that was the envy of the majors. Island essentially forced most of those labels to start signing more adventurous acts; thus, the imprints from the majors with more psych or prog sounds, e.g. Philips formed Vertigo, etc. Lots of great stuff on Island from the era.