Sorry for not getting back to you sooner. The short version of my answer is something like: to me Pragmatism is more like an attitude or orientation than a claim. If it were a claim along the lines of a definition of truth or reference in terms of practices then it would be circular as you note. But pragmatists do not (usually) presume to define truth and reference (i.e. what they are); rather they tend to explain the way we use those terms, and then (usually) argue that looking for more than that is a waste of time. At the extreme this means that concepts like truth and reference are vacuous; they are not properties, have no substantial role, and have no explanatory value. Do a little searching on "deflationary truth" for more on this.
Most (all?) pragmatists are anti-foundationalists, by which I mean they do not offer a "better" foundation (or "claim") than the old ones; rather they reject very idea that we can get at such a foundation. Not that they disprove it or deny that some such may exist. Maybe a foundation exists, maybe not, but either way arguing about it is a waste of time.
So "how pragmatism can explain the content of its own words and standards"? By explaining how that content is instituted by and illustrative of our practices, not by appealing to concepts like truth and reference. The nice thing about this is that is naturalistic, and so compatible with natural science - explaining our practices, which are naturalistic, is something natural science can (in principle) do.
Note that terms like "practical bearings" or even "practices" are not philosophically mysterious, unlike semantic vocabulary like "truth". The practices of a linguistic community are analogous to the behavior of a population of non-human creatures or of a system of non-living particles: something that can be observed and described scientifically. So there's no circularity in using such terms to describe how we explain our practices.
BTW, the risk of circularity was/is indeed well known to praggies, and the issues are actually much more complex and subtle than I've indicated. Plus there is more than one such risk. For a detailed argument about a possible circularity in the way pragmatists use semantic vocabulary like "true" and "refers" ("semantic" vocab being terms that purport to get their significance from representational relations) see Huw Price's response to Horwich in Expressivism, Pragmatism and Representationalism.
Hope that helps. FWIW the best intro to contemporary pragmatism that I know of is Pragmatism by Michael Bacon.
Edit (in response to comments): Consider Wittgenstein's famous dictum "meaning as use". That's a slogan, but it is often offered as a kind of definition, "meaning is use". The problem is it looks like a definition of meaning, which it is not, and the word "use" inevitably suggests instrumental use. But the kind of practices involved are not necessarily instrumental, at least not for the individual. E.g. "Ouch!" - there's no goal achieved by squeeling that, as far as I can see. It's easy to imagine many less elementary cases.
Replace "meaning as use" with "practices explain signficance" and you get closer to contemporary pragmatism. More technical: normative practices institute conceptual content. It's really the normativity that makes the difference. Here the risk is infinite regress: to apply a first-level rule, you have to have a 2nd-level rule telling how to apply the first-level rule. To apply the 2nd-level rule, you need a 3rd-level rule, and so on ad infinitum. This is where practice comes it: it halts the regress. At some point we say "that's just the way we do things around here." So practice is the unexplained explainer.
The normativity of practice is instituted socially, by punishment of deviation from norms and reward of conformance. If you use a word in a way that does not conform to community standards your interactions in the community are more likely to result in failure. This is where Pragmatism is deeply related to evolutionary thinking.
As to circularity and the need for Pragmatism to explain its own terms I guess the question would be something like, if normative practices explain conceptual content, then what is it for normative practices to explain the conceptual content of "normative practices". Point one: we've already rejected the idea that we need to explain some mysterious semantic relation between the term "normative practices" and something in the world that we describe using that term. Second, it's not the term "normative practices" that does the explanatory work, its the practices themselves, which can be observed and studied scientifically, unlike whatever it is that "true" and "refers" are supposed to mean. So in looking to our practices to explain our term "practices" there is no circularity. Just think of it as "look at what we do when we employ the term 'practice' and that will tell you what the term 'means' (to us, at least)"; this does not require an antecedent definition of "practice" that needs explanation. Or maybe think of "normative practices explain conceptual content" (or whatever your preferred pragmatism slogan is) as a methodological recipe rather than a definition.
Dunno how convincing that is but it's about the best this non-professional can do. If you really want to dig into this I highly recommend Bacon's Intro or Robert Brandom's Articulating Reasons. FWIW reading Brandom changed my life, no lie.