InDesign cannot open PDF without a special plugin. The normal workflow is to place PDF the same way you would place a graphic so that it is just another picture.
With one of the commercial plugins you can open the PDF file and edit the content in ID.
I was rapidly coming to that conclusion when I saw a number of them in a
Google search. Is there one you would recommend?
As far as I know, there are only two, and I've never used either one. You should see if you can find some reviews -- I take the vendor claims for retaining styles information, if any, with healthy dose of skepticism, for example, but I've got nothing to back that up.
My impression is that they work quite well if you have no other options beyond starting from scratch, but that you need to expect to do a fair amount of work rebuilding a real structure.
What I've been doing is converting some pdf books into pubs to read on my
Kobo (like a Kindle). There's a great online Free tool for doing this, but
it's limited to 25 Mbytes. That gets most of my books converted, but I have
a couple that are over that limit.
There is Recosoft and Markzware who have professional PDF to InDesign conversion tools. Markzware, whom I represent, offer PDF2DTP, which has the years of desktop publishing conversion, preflight and packaging technolgy behind it and will even also import native .AI files, in addition to PDF to InDesign CS6 or soon also InDesign CC.
Here is a video demonstration of PDF2DTP PDF to InDeisgn
I've used Recosoft's PDF2ID many times. Works well on some PDFs including a 120pp catalogue that I converted, other times not so good, and a waste of time on some, you'd be quicker starting from scratch on those.
I've not used Marzware's offering though their Q2ID plug-in is excellent and means I'll never have to touch Quark Xpress again!
Feel free to download a Trial version of PDF2ID Professional v3.5 from the Recosoft web site at www.recosoft.com. It will give you an indication of what the converted PDF file will look like using PDF2ID.