Public libraries are run by the local county/district/borough council, so there can be variations in policies as to what books they carry, fees that they charge, and so on.
In general, I've never heard of any library charging a fee to join (although I can't guarantee that's the case everywhere these days). They will normally just ask for some sort of ID which shows that you live in their area. Most (all?) libraries are now on computer databases, so you just get a credit-card sized library card with your name, barcode, etc.
You can generally take out from 4 to 8 (sometimes even more) books at a time, depending upon the district. The "due date" might be a week, two weeks, or longer, again depending upon the library district in question. You can normally "renew" a book after that time for a similar period, unless somebody else has requested the book and is waiting for it.
A card issued at one library can normally be used at any other library within the same district, so if you have two or more branches close by you can get a wider selection of books straight off the shelves.
The libraries also provide a request service to obtain a book from another branch. This is where there is usually a nominal charge, maybe 50 pence or £1, and obviously it might take a few weeks for the transfer.
There is also an inter-district transfer system in place which lets one library district borrow from another, so if you request a book and it is not available within your own area they can often obtain it from elsewhere. Sometimes this is covered under the initial fee, sometimes there's a small extra charge for this service. Sometimes books obtained this way have a time-limit on them, i.e. you can't keep renewing indefinitely, even if nobody else is waiting.
For really obscure books, they can even try to obtain a copy from the British Library. I've had that done several times in the past
Smaller libraries in more rural areas often don't have such a wide selection, as as you would expect, but on the whole, the library districts I've used are pretty good and quite helpful. And believe me, I've asked for some books that would be deemed
very obscure by most people (A Detailed Exposition of the British Post Office Telephone System, First Edition, 1949 anyone?).
These days, many libraries also offer internet access and rent video tapes too, although as these are deemed "extra" services there is normally a charge for these.
In the more rural areas the library service may also send a van around to outlying villages. Obviously the selection on board is very limited, but with the request system it provides a good service for those with limited transport.
So on the whole, I'd say that the public library system in Britain is pretty good.
P.S. Perhaps I should qualify this by saying that I have no recent experience of the library system in large urban areas. I've been out in the sticks a good many years.
