First Edition AD&D -- Finding the Rules
TSR kept the first edition of Advanced D&D in print from 1977 to the mid-1987. While they are now out of print, copies are easy to get (and often very affordable, especially the core rulebooks as lots of copies were printed) on eBay -- click here for more information on buying First Edition AD&D items on eBay. Used copies of many AD&D rulebooks are also available via Amazon.com at very reasonable prices. Copies in PDF format are also available for US$5 or US$6 a book.
Fan Rules Restatements
Fan "restatements" of older editions of D&D using the Open Gaming License and D&D SRD from Wizards of the Coast have become fairly popular in recent years. OSRIC is a restatement of the rules of First Edition AD&D. The first edition of OSRIC is fairly minimal, but the upcoming second edition is quite complete. While OSRIC has minor variations from the original TSR First Edition Advanced D&D rules, it is so close that it is a no-brainer to run published First Edition Advanced D&D adventures with them. OSRIC available as PDF files for free or as low-cost print-on-demand version.
What Rules Do I Really Need?
The first edition of AD&D has a large number of rulebooks, however, most are not necessary to play the game. If you are a player, all you need is a copy of the Player's Handbook. One copy of the Player's Handbook can even serve for several players in a group. The Dungeon Master needs a copy of the three "core" rulebooks: the Player's Handbook, the Dungeon Master's Guide, and the Monster Manual. The first edition of OSRIC can substitute for the Player's Handbook in a pinch and the upcoming second edition of OSRIC can subsitute for all three core reulebooks -- pdf copies of OSRIC are free.
If one buys pdfs or carefully selected used copies, one can easily get started running a first edition for around the cost of a single new core rulebook for the current edition of D&D! If you go the PDF route, you could easily also get a copy of the Temple of Elemental Evil megamodule -- a classic campaign setting designed to take characters from just rolled 1st level characters to about 8th level -- and still be under the price of a single new core rulebook from the current edition of D&D.