>>>What generates this amount of energy?
Star Trek ships use antimatter as main source of of energy + some complicated technology to maintain a stable reaction and transfer power around the ship.
>>> How much energy does a ship consume?
From the Technical Manual, paraphrased: (The Galaxy Class has thirty antimatter storage pods), each having a volume
capacity of 1,000 cubic meters. now, going from the antihydrogen having the
same mass as hydrogen, therefore weight, and using a standard of storing it at
-257.87 at 1 atmospheric pressure... the weight of hydrogen in just one pod is
And the tech manual says this: the galaxy class uses it all in about three years... meaning that, taken literally, it would burn through about 1,940 kilograms of anti-matter... per day.
1940 kilograms of anti-matter per day can generate A LOT of energy.
To be precise this is equal to 3880 kilograms of annihilated matter which equals to
3.492 x 10^20 joules
As a comparison the explosion of the Little Boy atomic bomb generated:
4.184 × 10^12 joules
So every day a Galaxy class ship consumes the same energy equal to about 83 millions Little Boy atomic bombs.
(a better question would be - what does the ship do with the energy when sitting "idle" i.e. not at warp ... most probably they have a system to reduce the energy production and actually going and running at wrap consumes much more energy than the "average" one)
>>> How much would it cost nowadays in US dollars?
A lot :)
Depends how you calculate the price - prices for gas, for electricity or for gasoline. Also is it retail price or production price.
If we take electricity retail price then as per http://www.statista.com/statistics/183700/us-average-retail-electricity-price-since-1990/ it was about 10 cents per kilowatt hour.
One kilowatt hour is equal to
3.6 x 10^6 joules
For one day a Galaxy class star ship generates (and consumes) about
9.7 x 10^15 kilowatt hours
Taking the above price this is about
9 700 000 000 000 000 dollars
9 700 000 000 million dollars
9 700 trillion dollars
As a comparison again - an estimation of the World Bank is that the world GPD for 2013 is about 75.59 trillion dollars.
Of course this comparison is irrelevant.