Being a student and not having owned a property before, the following is how I believe U.K council tax works through my general political knowledge and from my parents. Some of it may be incorrect.
Here in the U.K, we have a council tax. For England at least (not sure about other regions of the U.K, with their devolved bodies) it is the only tax set by local government. The basis of the tax is on property value, valued in the 1990's and it has several bands (A-H). Using the government's online council tax band checker, my family's house is in band g. From Wikipedia, I've copied the bands.
A up to £40,000 6/9 67% £845
B £40,001 to £52,000 7/9 78% £986
C £52,001 to £68,000 8/9 89% £1,127
D £68,001 to £88,000 9/9 100% £1,268
E £88,001 to £120,000 11/9 122% £1,550
F £120,001 to £160,000 13/9 144% £1,832
G £160,001 to £320,000 15/9 167% £2,113
H £320,001 and above 18/9 200% £2,536
As for local government spending, council tax only makes up a fraction of the revenue (I remember reading somewhere it is usually only 20-30%). The rest is handed out by the central government. I don't know about the rest of the country, but here in Winchester, local governments provides amongst other things: education, libraries, transport, refuse collection, fire service, road maintenance and police.
