The New York Law Journal is the principal legal newspaper for the New York City legal community and the paper of record for New York's First and Second Departments (i.e., the New York City metropolitan area). It is the only place to find many lower court decisions, and it is often the first place to publish new court rules.
All NYLJ articles are published in the print edition (also available on microfilm and a ProQuest digital microfilm edition). Articles are also available on Lexis (August 1991-present) and the NYLJ website (subscription required).
The full text of cases were published in print from the first issue until Fall 2010. After that, the print has only summaries. The full text of cases is available only on the NYLJ website (covering 2005-present; subscription required) and Lexis, in the New York Law Journal - Caselaw database (starting in 1989 but with a gap from January 1, 1990 - March 31, 1990).
If you need something from the print edition (e.g., an advertisement or an old article), the libraries at ABCNY, NYCLA and most law school libraries in New York City will make copies. They may also be willing get more materials from NYLJ website.
If you need something from an old print edition but don't have an exact citation, you can hire a researcher at NYPL Premium Services to look through the papers, microfilm or indexes (discussed below) for you.
For information about the NYLJ as an unofficial case reporter see "The New York Law Journal's Utility as a Reporter of Lower Court Decisions in the 21st Century," 34(4) LLAGNY Law Lines 30 (Summer 2011).
Indexes: You can find old cases and articles published in the NYLJ using the New York Law Journal Digest-Annotator. The Digest Annotator goes back to 1982, and it is available in print and online, by subscription through the NYLJ web site.
In addition, you can find NYLJ articles indexed back to 1980 in the Legal Resource Index (LRI) and LegalTrac. The LRI is available on Lexis and Westlaw. The LRI and LegalTrac are also sold as a subscription database, available through some academic, bar association and membership law library web sites.
You can find where cases were published in the NYLJ from 1888 to 1982 using Clark's Digest-Annotator, the predecessor of the New York Law Journal Digest-Annotator. The books are available in some New York law libraries with historical collections, and microfilm is available at others, including New York Public Library's SIBL branch. If you don't have access, you can hire a researcher at NYPL Premium Services to look up cases for you.