At the moment, generally you use GET and ask for a different Content-Type with an Accept header, or you say something like <link rel="alternate" type="application/rss+xml" href="foo.xml" />. In some cases you're expected to guess the alternate URL instead, maybe based on a document somewhere else, which is non-RESTian. However, it's pretty rare for someone to do what you suggest, which is to use new HTTP verbs in order to get different representations.
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At the moment, generally you use GET and ask for a different Content-Type with an Accept header, or you say something like <link rel="alternate" type="application/rss+xml" href="foo.xml" />. In some cases you're expected to guess the alternate URL instead, maybe based on a document somewhere else, which is non-RESTian. However, it's pretty rare for someone to do what you suggest, which is to use new HTTP verbs in order to get different representations.