The header of a FITS file is ASCII, and points you to further information. Calling
head -n 1 example.fits directs you to "'Astronomy and Astrophysics', volume 376, page 359; bibcode: 2001A&A...376..359H".
A software to view FITS images is ds9 (yes, that makes it hard to google...). Alternatively, there's skycat.
Both can be used to view and do basic analysis on FITS images.
For FITS binary tables, it is probably best to write your own analysis software. For a quick look, fv might do the job.
Accessing the data yourself
If you want to write your own software for analysis, take a look at either cfitsio, a C library for reading and writing FITS files, or pyfits, a python module which does the same and which seems to have merged with the astropy software package. The cfitsio page in the link above has links to documentation on both the cfitsio library and the FITS standard in general.