I've used something like FOIA and a friend has used FOIA on a project we were involved with. With my request, I knew quite precisely what I was seeking: A letter from one government department to another. They first sent me the wrong one, then when I re-requested it, they sent me the correct one. It was all done by email (I received PDF scans of the letters) and took maybe 7-10 days.
My friend was looking for much more information - in the end it was several hundred pages. It took many months, partly because I think there was some internal wrangling before they sent it to him. But it was also emailed, which was good because there's a charge for printing. This way it was free.
Another friend also made a request under a similar law to FOIA, and got incomplete data that resulted in a fairly long correspondence with the sender, which yielded more data and finally the realization that the record-keeping had been pretty bad. (The department concerned *should* have kept complete detailed records in a standard format, but didn't.)
From the outside, my perception is that usually what's being requested has the potential to be used in ongoing battles; and so sometimes the organizations receiving the request try to stall. In the end, they do give the information; both my friends had to follow up and be quite persistent.
I think it helps if you can specify the document you are looking for - I guess it makes it easier for people like Miguelito who actually do the work of digging out the material.
I understand the problems in getting this information, but I think it's just amazing that such a facility exists. It really feels like *this* is democracy.