The problem with other answers is that Stack Exchange API is GZIP'd and url.el shipped with Emacs does not automatically decompress it.
Take a look at my request.el library which supports automatic decompression (to be honest, I just added the support). Here is an example to fetch the most active question in stackoverflow:
(request
"https://api.stackexchange.com/2.1/questions"
:params '((order . "desc")
(sort . "activity")
(site . "stackoverflow"))
:parser 'json-read
:success (function*
(lambda (&key data &allow-other-keys)
(let* ((item (elt (assoc-default 'items data) 0))
(title (assoc-default 'title item))
(tags (assoc-default 'tags item)))
(message "%s %S" title tags)))))
request.el is well documented, comes with executable examples and is well tested.