The value is determined by some sort of average between the price people are asking if a seller wants to buy and the price the wants to pay for that Bitcoin. Shorter: supply and demand.
But I guess that you know this and want more. You should have searched. For example, a nice answer comes from 2013.
You can search more with google using something like value of bitcoin site:bitcointalk.org

basically the value of cryptocurrency is determined by the demand and supply of the market price. before being able to invest in ICO should do detailed research on the project, many interesting ICO projects and can provide many benefits if we can invest in them. suggestions and recommendations of people can indeed be an option but the most important to decide before you can invest in a big project, only yourself can decide it by understanding the white book provided by the ico project

Valuing a cryptocurrency is difficult to do beyond supply and demand. We can work in the growth of the money supply as a factor of supply, but demand is hard to calculate with accuracy.

And to be fair, fiat currency is hard to value as well, but fiat currency has the strength of the Nation it represents (e.g., gross domestic product, trade balance, etc.) Cryptocurrency doesn't have that and at large fiat currency is only backed by the full faith and credit of the country that issues it.

Another criteria that complicates crypto valuations is the global scale of the network. News is a great indicator of the strength or weakness of an investment, however those markets are usually localized. A global market is immensely difficult to monitor or assess how much one negative news item may impact demand globally.

There is no central authority that determines the price of something, the value of something in a free market it is always an agreement between the buyer which is willing to pay a certain price for an asset and the seller which is willing to sell his asset for a price, so the price you see in the market is nothing but the current agreement between buyers and sellers but this can change at any time for any reason.

if I also do not agree if the bitcoin price in tetepkan gan.
just my suggestion bitcoin price if it rises little by little.
so also if the price again down should be gradually do not jump free.

Its quite easy to determine value of crypto currency when you will buy something with crypto that time you will know the value of it also the  facilities if you need more suggestion you can see in website for better result also ICO is related with project which encourage people to invest.

This thing is all about crypto market and this is like stck market if you understand share market then it will be understandable too because based on market data or news you can know about how to determine value also this is related with sellers and buyers transactions.

The value of cryptocurrency is dependant upon many factors. Among them, the demand and supply of coins plays a major role. Besides many other factors also play role.

as in any other market, demand generates supply, the more promising the crypto currency, the more its price

In cryptocurrencies the price is determined only by demand/supply nothing more.
the instrinsic value of an asset in general or cryptocurrencies in determined by other factors!
usually in the long run the price of an asset should correspond to its instrinsic value!!
So, recap : price in short term is determined simply by demand and supply movements.
in the long term the price is determined by the instrinsic value of the asset!
cheers!