Hi Joyce!
"Go to the dogs" is an example of a "pun" or a "play on words", a phrase that can be understood in one of two ways (maybe more!). Sometimes they are called "double entendres" (in french, "Double Sans", literally, "double meaning")
When trying to figure out what the writer is trying to say, always remember that one meaning of the phrase can be derived from the actual words themselves! In this case, the literal meaning of "going to the dogs" is actually "going to the dog races"!!! like going to the horse races!
LITERAL MEANING of "going to the dogs", is "going to the dog races"
PHRASE MEANING is the one you identified which is something not being as good as it used to be...eg "Arsenal football team have really gone to the dogs!"
In our example the headline "going to the dogs" refers to "going to see The Dogs"!!, The Dogs are a music band.."..promoted to Razorlight's main support" (ie they have been given the honour of playing a few songs at a concert before Razorlight comes on)
In this case the secondary meaning of "going to the dogs" is not applicable, but it has been used in the headline for yet an extra, third layer of meaning! And this is that, Maximo Parks were originally due to support Razorlite but as one of the band members broke his arm, the support act has now "gone to The Dogs"!!! ie, they have been given the place instead of Maximo Parks.
So, lets look briefly at your other example, "college dorms go to the dogs"
LITERAL MEANING - maybe college kids going to the dog races, or maybe a dog show
PHRASE MEANING - college dorms are just not as good as they used to be, maybe they're smaller, more cockroaches!!
Remember the pun doesnt HAVE to mean that college dorm kids went to the dog races, just that dorms are worse than they were. You have to look at the context of the surrounding sentences to see which meanings might apply.