Know what records are available at the facility – types, date ranges, etc.
Know if any costs are required, including photocopying and if a membership is necessary
Know the hours that the facility and its materials are available to the public
Know whether the library has an “open stack” or “closed stack” policy for obtaining books
Bring any reference materials you may need while at the facility
Bring a detailed list of what you are expecting to find, including all necessary documentation
Bring a wish list of what you would like to find
Bring any personal items you might need: reading glasses, magnifying glass, paper clips, stapler, folders, etc.

Here is a link to what is called "Repositories of Primary Sources: http://www.uiweb.uidaho.edu/special-collections/Other.Repositories.html. No guarantee on all of the links being active.

Libraries

Many libraries allow you to do research on their web sites.

See www.genealogy.about.com/cs/libraries/ for specific information about selected libraries
For a directory or links to U.S. libraries see the following web sites:

Top genealogical free public libraries in the U.S. (ranked in order of materials available):

Allen County Ft. Wayne Public Library, 900 Webster St., Ft. Wayne, IN 46801, 260-421-1200, www.acpl.lib.in.us/genealogy/.
[IT'S TRUE! Fort Wayne, Indiana has the best genealogical public library in the U.S.!
That is a fact, not an opinion!]
New York Public Library, 5th Ave. and 42nd St., New York City, NY 10018, 212-930-0800, www.nypl.org
Newberry Library, 60 W. Walton St., Chicago, IL 60610-7324, 312–943–9090, www.newberry.org
Boston Public Library, 700 Boylston Street, Copley Square, Boston, MA 02116, 617-536-5400, www.bpl.org
Los Angeles Public Library, 630 W. 5th St., LA, CA 90071, 213-228-7000, www.lapl.org
Detroit Public Library, 5201 Woodward Ave., Detroit MI 48202, 313-833-1000, www.detroit.lib.mi.us/
Dallas Public Library, 1515 Young St., Dallas TX 75201, 214-670-1400, www.dallaslibrary.org

U.S. state libraries: for a list of their web sites visit www.dpi.state.wi.us/dpi/dlcl/pld/statelib.html

Genealogical Societies

Their web sites usually offer limited but good information, even for non-members.

Join national societies and get their publications
For links to many U.S. genealogical societies see the web site www.obitlinkspage.com/hs/
New England Historic Genealogical Society (NEHGS), 101 Newbury Street, Boston, MA, 02116, annual membership is $75 www.americanancestors.org (growing collection of material available online for members with one master index for all)
National Genealogical Society (NGS), 4527 17th Street North, Arlington, VA 22207-2399, annual membership $50, www.ngsgenealogy.org
Daughters of the American Revolution (DAR), Washington, D.C., www.dar.org/natsociety
Sons of the American Revolution (SAR), Louisville, KY, $35/year, www.sar.org
The American Genealogist (TAG) (a leading genealogical publication) www.americangenealogist.com/, $30 for 1 year or $56 for two years or $80 for 3 years

For a list of genealogical societies by state see the web site www.obitlinkspage.com/hs/
Western Reserve Historical Society, 10825 East Blvd., Cleveland, OH 44106, www.wrhs.org [known as one of the top genealogical collections in the U.S.]
New York Genealogical and Bibliographical Society, 122-6 E. 58th, New York NY 10022, www.nygbs.org [known as one of the top genealogical collections in the U.S.]

Books and lists finding aids exist for this including Val Greenwood's book part of which is excerpted at www.genealogy.com/genealogy/5_grnwd.html
Also see the appropriate chapter in Ralph Crandall’s book Shaking Your Family Tree
Family History Library of the Church of Jesus Christ of Latter Day Saints (aka. LDS) facilities in Salt Lake City or visit any of their local Family History Centers (go to the web site www.genhomepage.com/FHC/all.html or look in the phone book under “Church of Jesus Christ” for the family centers. The Salt Lake facility is H-U-G-E (it’s hard to overstate that!!!). Both the New England Historic Genealogical Society of Boston and the National Genealogical Society of Washington, D.C. sponsor annual trips to the LDS Salt Lake facility for their members. Books exist that explain how to research in the Salt Lake facility. One book is Your Guide to the Family History Library: How to Access the World's Largest Genealogy Resource by Paula Stuart Warren and James W. Warren, $20

WARNING: much 'junk' can also be found of these websites. Use many grains of salt with their information.