Income taxes, sales taxes, and property taxes are each treated separately.
Sales Taxes are dependent on local and state law and are generally pretty similar across the country. There is often some variation on certain things such as dues (is it actually providing a service a la prepaid greens fees, or is it dues?) and cart fees (is it a product or a service?).
Income taxes depend on the type of course. Member owned 501 (c) (3) non-profits generally pay no income taxes, but do have to file a return. Municipalities pay no income taxes, unless leased out to a private operator, who do. Everyone else pays based on their corporate structure (LLC, corp, etc.)
Property taxes are much more of a wildcard. Municipal courses generally do not pay property taxes because it would make no sense for a municipality to tax itself. Interestingly, that usally also carries over to muni courses leased to an operator.
Depending on the jurisdiction, property taxes can be based on either the market value of the property or the cost of the improvements. Most areas now use the market value, which is determined first by an appraiser using a variety of techniques. If you don't like the assessed value, there is usually some sort of appeals process where you hire your own appraiser. It's a little difficult to value member owned private clubs, but it can be done.
That is, unless you live in Nassau County, NY. In that case, the taxing authority decided to jack up the property on all of the private clubs there with some rediculous assessed values. The clubs got together, appealed, and won their case. Tax rates were dropped by a significant amount, helping the clubs there by. However, the assessor struck back by immediately reinstating the taxes the next year, forcing the clubs to appeal again. I think they won again, and reportedly the judge was very angry at the assessor, but haven't heard anything recently. Another club in Nassau appealed and won, and is expecting a seven figure check to reimburse past wrongs.