What are some different methods for pricing electricity? I know that in New Zealand, the wholesale price of electricity is set using a spot market, whereby every half hour, each of the electricity producers provide offers for how much electricity they can supply at each price level, and then when the actual amount of electricity is used, they producers are paid at the highest value need for all units of electricity supplied, with the lowest offers being utilised first.  

The market is regulated by the Electricity Authority, which is an independent crown entity, while the transmission of electricity is managed by Transpower, which is a state owned enterprise. 

In practise what this means, is that the producers will offer their renewable energy for free, and price their coal/oil at a higher rate. Some coal/oil is always needed and so this higher rate is determines how much the producers are paid for their cheaper energy supplied. 

My question is, how else can and are electricity prices determined around the world?
In most of Europa the physical price for electricity is determined in day-ahead spot auctions. Essentially it is a free market, where anyone can buy and sell power, given you that you can fulfill the regulation set forth by the different national power exchanges and system operators. 

This means that every day before 10.00 - 12.00 AM all producers and consumers must have told how much power they wish to sell and buy. From 12.00 and to around 12.42 a number of welfare optimization algorithms are run. After this, the different power area prices are published, along with the supply and demand curves for almost all countries. 

In essence it is a where supply meets demand. This is complicated a lot by different bid-types, power connections across borders, physical constraints on cables and so on, but you can download the newest curves from Germany and France each day from epex.com if you want. 

Because there is a lot of competition, you will mostly see power producers selling their power at their marginal costs. Because of subsidies this means that renewable energy sells as low as -300 euro pr. MWh - yes, they actually in some cases pay people to take their product. Nuclear and lignite power is around 10-18 EUR, the comes cheap coal and hydro (depending on season), the more expensive coal, gas and finally oil. From the price you can more or less tell which kind of production is running in any given hour.