How the prices go up and down is simply affected by the result of demand and supply. When the demand of the coin is really high, then there is a great chance that the price or value of the coin would relatively increase. Meanwhile, if the demand of the coin is less, that is more people are rather dumping the coins rather than buying, then there is a great chance that the price of the coin would reduce.
That is the general principle of economics when it comes to demand and supply. Certainly, it is a market and all that is going on is more like an auction and everyone trying to bid on how much they want to end up selling and how much they want to buy.
Now, all these things are certainly a prerequisite to how people perceive the market in that particular space of time that they are buying, which is either the demand is huge or supply is on the high side, so with that, we see the market tending towards whoever is winning. Crypto market is not just this market as that is generally applicable to every other market outside cryptocurrency, such as Forex, stock market etc.
With any market, the law of supply and demand will always be applicable and in this case as long as there will always be people buying and selling in the market, the price will always fluctuate and the position at which it fluctuated towards is dependable on which of the sides have a larger effect on the market due to their huge presence.