You can find most of the information you need about court clerks and court houses from the respective court's web site. You can use FindLaw to link to most Federal and state courts, or you can just search Google or another search engine.
If you need information on many courts, or if the information you need isn't available on the court web site, you may want to use a directory, such as BNA'S Directory of State and Federal Courts, Judges, and Clerks, Your Nation's Courts Online (CQ Press), the Judicial Staff Directory (CQ Press), and/or the The Judicial Yellow Book (Leadership Directories).
New York Court Clerks and Court Houses are listed in the Second Circuit Redbook.
Law Clerks: Unlike court clerks, judges' law clerks generally change every year or two, so the law clerk listings in most directories are out of date. To find the name of a judge's current law clerk or clerks, check the court web site, call the judge's chambers and/or try to look up a list of law clerk in the jurisdictions legal paper of record (e.g., in New York City, look in the New York Law Journal, starting around September and going into at least October). To find the name of a judge's prior clerks, search back articles from the relevant legal paper of record and/or check back editions of the the general clerkship directories discussed above. For older information, you can also check back issues of the NALP Judicial Clerkship Directory and/or the NALP State Judicial Clerkship Directory (both of which were discontinued around 2004).
To find out what clerkships are available on the Federal level, see USCourt.gov. For state courts, see The Guide to State Judicial Clerkships and the web site for the relevant court system.
For more information about the general practices of particular judges on hiring clerks --including how many, when, whom to contact, what documents to submit -- try Behind the Bench: The Guide to Judicial Clerkships (NALP), as well as the sources discussed on JudicialClerkships.com and NALP's Judicial Clerkship Info for Career Services page.