The DFSG is a statement of intent (so are the "Four Freedoms" of the Free Software Foundation).
Each piece of software (and there are many) has a license.
Whether the license agrees with the DFSG is, actually, a judgement call. Generally, I'm happy to go with the judgement of the people who put Debian together, and with the judgement of the Free Software Foundation (it's worth noting that the two don't always agree, on some subtle points). All in all, it's a judgement call best made by people with legal training: there's no need to read each individual license before using the software. If the program is in Debian, several people have read its license and agreed that it meets the DFSG. And those are people who (a) know what they're talking about, and (b) are usually very very strict about the application and intent of the DFSG.
However, if you want to do more than use a program: if you want to modify a program, or write a new one based on it, or write a program which uses another program, then it probably is worth your while to actually read the licence, especially if you then want to distribute your modified program. Any program which meets the DFSG will allow you to modify it as above, but the precise conditions under which distribution is permitted will vary from one license to another.
P.S. That article about Christianity and Free Software was interesting. Thanks, Gervase.