to get it done properly, you need to have an internet connection in every library, and to have your networking guy set up vpn routers (cisco ASA is the best choice)
set up a vpn between all libraries, and of course set up proper routing between all the vpn'd subnets
some ISPs can provide the vpn functionality on their own level, that costs money, but might be better than your own vpn
topology, in this scenario is a bit of a too basic question, you need to think of an implementation
if you don't know how to set up VPNs, routers, NATs etc - get an IT professional to help you, this is serious stuff.
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