This is exactly where anyone coming to Heidegger for the first time ought to start. Unfortunately, for many people it's also infuriatingly difficult to unpack, due to Heidegger's style. For example:

"The discussion of Being as just that -- Being -- still speaks an inadequate language, insofar as, in our perpetual references to Being itself, it is addressed with a name that continues to talk past Being as such. In making this remark, we are voicing the assumption that Being -- thought as such -- can no longer be called 'Being.' Being as such is other than itself, so decisively other that it even 'is' not."

This obscure ditty[1] is from Nietzsche, Vol. IV. The key, as you point out, is to focus on the 'is' and, equally importantly, the 'as'. Replace "Being" with "the hammer" or some other object and things start to clear up, at least a little bit. The insight is that that thing in the carpenter's hand exists 'as' a hammer (for the carpenter, for you, for me), but it 'is' not a hammer; the 'is' of a thing is simply an 'as', a way of being in a world. A world or a way of being in it can change, and then the hammer 'is' something else.

A seemingly small insight, to be sure, but it's Heidegger's point of departure, and has a wide range of practical applications in later thinkers, even ones working on the sciences (e.g. Bruno Latour and others doing "sociology of science"). Deconstruction -- destruktion is Heidegger's word -- is on balance the practice of resisting what is given, of not falling "into the grip of ideas already decided beforehand"[2]. The clearest statement of this idea in Being and Time is I think in §32, which starts on H149. This is the starting line for basically all contemporary theories of interpretation, from Gadamer to Ronald Dworkin.

1. Of course there are reasons for Heidegger's writing the way he does. Whether or not they're good ones is a whole 'nother discussion.

2. "Language", from Poetry, Language, Thought.