You should put it somewhere in your local-texmf root (if you use TeX Live, you already have one; if you use MiKTeX, create one if not already done with MiKTeX Settings application).
More precisely, you should put it in:
local-texmf\bibtex\bst\
or even in
local-texmf\bibtex\bst\ieeetran
since it is an extension to the IEEEtran bibtex style, then refresh the filename data base.
But you also might consider using the biblatex-ieee package: the job of hieeetr is adding the eprint field to ieeetran bibtex style file – and this field is already defined in biblatex.
Added:
As pointed by @cfr, after the file(s) have been placed in the relevant place(s), you must refresh the FNDB (MiKTeX, with MiKTeX Settings), or run mktexlsr $(kpsewhich -var-value TEXMFLOCAL)(TeX Live).
~/texmf/tex/latex,.bstfiles should go in~/texmf/bibtex/bst. – Adam Liter Apr 07 '14 at 18:09~/Library/texmf/it will be something likeC:/Users/YOURUSERNAME/texmf, I think. – Adam Liter Apr 07 '14 at 18:12C:\Documents and Settings\<user name>\if you're running Windows XP. Joseph Wright's answer shows file paths for all major operating systems. Just replace all the/tex/latex/local/'s with/bibtex/bst/'s. – Adam Liter Apr 07 '14 at 18:17