Check that the licenses are free software licenses (some free licenses may be
missing from there, but most free software packages use one of these
licenses), and that the package has complete source code available. You can
check the license by downloading the source code. For the GNU licenses and
some other licenses, there should be a copy of the license itself distributed
along with the software; not complying with this requisite doesn't makes the
program proprietary; but it's a sign that the developer is sloppy about
licensing and he may unintentionally have included proprietary dependencies
or failed to unambiguously make his program free software. It must be clear
which license apply to each file. Just including the license in the source
distribution without further licensing information leaves uncertain whether
the license applies to the program, and hence it can not be considered free
software (See the GNU GPL FAQ).
Check the section How to Apply These Terms to Your New Programs in the GNU
General Public License. These are guidelines, though. It's not a necessary
condition to follow these guidelines in order for a program to be free
software, but it's a sufficient condition provided that entire package is
under that license, and that source code is included.
Some software packages have no license, and that makes them proprietary (See
the GNU GPL FAQ ยง No License). If you find software like this that would be
useful in a fully free system, consider writing to the author to make him
aware that because of the lack of license, his software is proprietary
(despite that he may have intended otherwise), and ask him to make it free
software (preferentially under the GNU GPL). This is almost always due to
indolence of the author, specifically, a disliking for Copyright law coupled
with the erroneous belief that ignoring it will make it not apply.
Note that sometimes there is object code in the form of human readable
programming language code. Notably, this is the case with Linux, but I don't
know of any other package doing the same.
Apart from being fully free itself, you should make sure that the program
doesn't has mandatory proprietary dependencies but this not necessary to do
explicitly if you have checked that the package itself is free and you have
no proprietary software installed (you would notice if that was the case
because the package will not compile or will not run properly).
