Generally speaking, 2e's core books attempted to take the sprawling mess 1e's system had become and condense it into a neat, orderly system.
And then TSR promptly glutted the market with supplements, turning 2e into a big, sprawling mess.
Typically speaking, there a 6 ways to play 2e. Each DM needs to pick the format he's comfortable with:
1.) Default. (Core Books only) AKA revised 1e. This version only uses the hardback books (PHB, DMG, MM, ToM) and occasional modules and such. Its pretty much like playing a easy to understand and clean version of 1e.
2.) Default + PO. Same as above, but adding the Players Option Books (C&T, S&P, S&M) and the DMG options (HLC) to the mix. This radically shifts the power and feel of the game and can lead itself to a very complicated (but still fun) system. DM's be warned though, there is MAJOR power creep here.
3.) Default + Complete Books. Again the default books are assumed, but this adds Kits and alternate rules from the Complete Books (Fighter, Priest, Wizard, Thief, Bard, Druid, Ranger, Paladin, Elves, Dwaves, Gnomes and Halflings) as well as some new classes/races (Psionics, Ninjas, Barbarians, Humanoids). Balance here gets splotchy; some stuff is too good (elven bladesingers) some too poor (Complete Priest Specialty Priests) so a DM has to be REAL careful what he allows here, for balance sake.
4.) Default + Setting. This assumes your using published setting (Greyhawk, Realms, Dragonlance, Dark Sun, Ravenloft, Planescape, Al-Qadim, etc) and all related supplements. Rarely did I ever see a setting where balance was greatly out of whack (well, Realm's Specialty Priests border on that) but overall this is what most people think of when they recall fond memories of 2e.
5.) Default + Complete/PO + Setting. Pretty obvious. Option four mixed with 2 or 3. The most inclusive, the hardest to maintain balance.
6.) Pre-3e. The last category. This version uses a lot of PO material mixed with some Complete and some Setting material to create something close to what 3e would become. It doesn't change overall systems greatly from the Default, but it does included revised spell/domain lists, additional classes/races, attacks of opportunity, new spells and magic items, and a hefty dose of house-rules. Many people playing from 1997-1999 played this out of necessity. Its also kinda a "anything within reason" goes and requires a lot of dilligence on the DM to keep fair play.
Subtle variants of each occur, of course. It also ignores wildly different houseruled versions. Note: Player's Options were generally designed to supersede the Complete line, so you rarely see the two in use together (barring odd exceptions like a Complete Humanoids Race or Psionics).