The March 2014 issue of Sky & Telescope features an article by Bob Cava, who hunts for quasars in light-polluted New Jersey with his 10- and 16-inch telescopes.
As Cava discovered, quasar hunting requires considerable skill with astronomical databases and online tools. This web supplement describes some useful resources and collects their URLs in a convenient form. Click here to jump to the list of URLs if you're not interested in the descriptions.
The first challenge is obtaining a list of quasars that are bright enough to see through the eyepiece of a backyard telescope. Then you have to "weed" the list for objects that aren't really quasars and objects whose magnitudes are inaccurate. And finally, since most quasars look exactly like stars through the eyepiece of a telescope, you need a detailed image to make sure that you're really looking at the quasar and not a star of similar brightness a few arcseconds off the correct location.
Wolfgang Steinicke's Catalogue of Bright Quasars and BL Lacertae Objects is probably the best single resource for amateurs setting out to observe quasars. It's in fixed-column text format, easy to import and manipulate with Excel. Note that in addition to quasars (QSOs) it includes some active galactic nuclei (AGNs) below the luminosity limit for quasars, as well as BL Lacertae (BL) objects. The magnitudes are not always reliable, and there is no indication of variability — some quasars and all BL Lac objects vary a great deal in brightness.
The East Valley Astronomy Club's Quasar Observing Program is considerably less reliable than Steinicke's list. It appears to have been compiled using messier45.com, which yields a good deal of useful information, but also includes many objects that are definitely not quasars. (Some came from a study that listed quasar candidates; others seem to be completely spurious.) Nonetheless, the EVAC program does include some bright quasars that don't appear in Steinicke's list.
The Frankfurt Quasar Monitoring Project website includes 10 of the 12 objects in Cava's list, as well as many others. A brainchild of German stargazer Stefan Karge, this website contains a great deal of information of interest to amateur astronomers. The visual magnitudes, obtained with classic variable-star observing techniques, are a useful supplement to and cross-check on the magnitudes listed in professional catalogs, which are not necessarily reliable. And the author has researched each object in depth, providing lucid summaries of information that would otherwise require weeks of effort reading through professional papers.
Most serious amateurs use the Digitized Sky Survey to obtain images for detailed star-hops. The DSS gives you precise control over the location and size of the field displayed and covers essentially the entire sky. (Sometimes one particular piece will be missing in one color, or from one survey.) But it is limited to displaying at most one square degree of sky at a time.
Wikisky is an amateur-friendly tool that synthesizes images from the red and blue DSS images (and, optionally, other sources). Note that if Wikisky doesn't recognize your object name, you can type in the coordinates, e.g. "12 29 06.7 +0 03 09" instead of "3C 273". Mouse over the Wikisky display to obtain information about the objects shown. Click on the camera icon near the top to capture Wikisky's displays in JPG format.
The Sloan Digital Sky Survey can be thought of as a modernized, improved version of the Palomar Sky Surveys that underly the DSS. For the sections of sky that SDSS covers, it's often the ultimate source. But it doesn't cover the entire sky; most notably, it avoids the Milky Way.
I find the SDSS Finding Chart Tool to be the most useful entrypoint to the SDSS database. It will accept coordinates in conventional form and convert them to decimal degrees, but you need to enter all three components of each, including arcminutes and arcseconds. Click on Explore near the upper-left corner to obtain data on the objects shown in the display.
If you want to do serious research, you need to become familiar with the resources used by professional astronomers: the three interlocking tools (SIMBAD, VizieR, Aladin) run by the Strasbourg Astronomical Data Center (CDS), the NASA/IPAC Extragalactic Database (NED), and the SAO/NASA Astrophysical Data System (ADS). These provide entry into the world of professional astronomical papers and databases.
SIMBAD and NED provide data about individual objects and, perhaps more importantly, give references to the data sources. One source that I relied on heavily for the magnitudes in the table for Cava's article is a 2009 paper by Roopesh Ojha et. al..
Amateur Quasar Lists