how many ways to hook up a subwoofer

If it's a powered sub there won't be any issues connecting it to the speaker output of the amp.  Connect the sub between the amp and the main speakers. Your amp won't have any additional stress because the sub's amplifier will be powering the sub. 

Contrary to popular belief, some engineers actually recommend using the speaker level input of the subs instead of XLR or RCA because then the audio going into the subs will match the voicing (sound signature) of your power amplifier and will be the same as the voicing going to your main speakers, instead of the voicing of your preamp going to a sub and the voicing of your power amp going to the main speakers.  RCA connections is not recommended due to their tendency to pick up noise caused by ingress and XLR is recommended for long runs to avoid noise issues, but regardless, speaker level inputs are the preferred method of many engineers, for the aforementioned reason. 

I sure don't want to argue with @ellajeanelle, as obviously is a nice person, but I am involved with pro and consumer both and I cannot figure out what you are talking about with "voicing" of speaker outs vs line level (-10 RCA) or pro level (+4 balanced).  ALL sub set ups in professional applications are +4 XLR balanced, this is the single safest way to do it, straight from the source preamp, using a "Y" cord to split the preamp output between 2 destinations: #1 to amp (then to main speakers)  and #2 to the sub. 

Maybe by your phrase "carrying voicing" you mean some of these highly colored preamps, like an old tube unit, where the line level out is already changed based on the tube circuitry inside the preamp?  That would be a case where the line level output DOES carry the color of the preamp as the only circuitry inside the preamp is tube.   But in the case of most modern or solid state units, the line level output labeled "tape out" or "preamp level out" or "subwoofer out" would be relatively color free.  

If you use the speaker level sub input, aren't you adding the preamp output color to the amp color to the speaker cable color and finally to the sub?   

Brad     

lonemountain:  You are talking about professional applications and not what's being discussed.  See 2:20 on link: The best way to connect a subwoofer (youtube.com)

 BTW: I have several systems, both HIFI and professional and I know what you mean.  They are all connected differently and speaking for myself, the difference is an audible improvement if connected as described in the video!  Try it!  This video will clarify my post.   Thanks for your input.

Paul McGowan on "High Level" sub connection