Sword Art Online 1: Aincrad tells the story from the start of SAO until the end:
after Kirito defeats Heathcliff and wakes up in the hospital.
Notably, it excludes the following arcs that were included in the anime:
- Sachi and the Moonlit Black Cats,
- Silica and Pina,
- Lizbeth the blacksmith, and
It excluded these arcs, and, as far as I can remember, it didn't add any new content. (Maybe just described events that happened in the anime in greater detail.)
Instead, the arcs listed above are each detailed in the following book, Sword Art Online 2: Aincrad.
In terms of time, the books do not present information in chronological order as the anime did. We know in order of occurrence, the "side" arcs are arranged as follows:
Sachi arc -> Silica arc -> Lizbeth arc -> Yui arc
where the events involving Sachi happened first chronologically and Yui, last.
None of these arcs are present in book 1, but they are presented in the following order in the second book, which is not in chronological order. I don't know the reason for the author/producer(s) switching the order around like they did, but it is:
Silica -> Lizbeth -> Yui -> Sachi
The stories themselves essentially describe events exactly how the anime portrayed them. I thoroughly enjoyed reading the light novels, although for the most part, the only thing you'll get out of reading them is slightly different wording/description of the same events. One exception that does come to mind is
they include a bit at the end of the Lizbeth arc detailing her reaction when Kirito defeats Healthcliff and she was finally going to be free of SAO. It wasn't very long - a page or two at most.
Admittedly, I didn't read the Sachi arc because I assumed I wouldn't have gotten anything new out of it.
I don't know the ordering for Fairy Dance (have them but haven't read them yet), but it's possible it follows a similar idea (for ALO). Here are links for Sword Art Online 3: Fairy Dance ("1") and Sword Art Online 4: Fairy Dance ("2").
I haven't read the progressives, so I don't know where they fit in.
Anime portrays events in near-chronological order, although the Sachi arc is a flashback.
SAO 1 LN leaves out a few arcs but tells the main story from the beginning of SAO to the end.
SAO 2 LN has 4 sections, each one an arc that was in the anime but not in SAO 1 LN. These sections are neither entirely in chronological order nor the order they happened in the anime.