There are a couple of ways to make money from cryptocurrencies.
Investing
The most popular is investing, similar to stocks. Many people (investors) have purchased various cryptocurrencies in the hopes that the cryptocurrency will increase in value over time. Anyone who had invested $10,000 in bitcoin in 2010 would be a multi millionaire today due to the value of the coin increasing over time.
There's an explanation in the price of Bitcoin module that covers why the price of bitcoin has been increasing.
There are other coins that have increased in value too, some for the same reasons as bitcoin, and investors have purchased them waiting for the price to increase. Once the price increases, they sell to enjoy the profits.
Many of these investors are long term holders, meaning they are only looking to sell in a few years after the price of a cryptocurrency matures quite a bit.
Staking
The 2nd way of making money with cryptocurrencies is to invest and stake a Proof of Stake cryptocurrency. There are 2 major algorithms in cryptocurrencies. The first is called Proof of Work and Proof of work (or PoW) is applied when mining computers are trying to produce a working hash and are rewarded for doing so. Proof of work is resource intensive.
Proof of stake (or PoS) is a cryptocurrency algorithm that rewards participants for "staking" In this process, a person buys some cryptocurrency, then transfers it over to a desktop wallet on their computer and they leave the wallet running and computer connected to the internet. The wallet will download a copy of the blockchain and act as a node.
The participant then proves that they are staking because their wallet then joins the blockchain and the rest of the network can see the coins are being staked, the participant is then rewarded for staking. The stake reward differs from coin to coin with some of them offering up to 10% per year which is paid out at regular intervals and is compoundable - meaning that their rewards get added to the amount they are staking and the stake reward grows over time according to how many coins are being staked - the more you stake, the more you are rewarded.
People can then sell their profit or continue to compound.
Trading
A 3rd way people make money from cryptocurrencies is to trade. Trading is an art that can be learnt and is covered in great, great detail in the Trading module. Trading essentially involves buying at one price and then selling for a higher price. There are many traders all trading at the same time, some buying, some selling - the goal of every trader is to make a profit on every trade. Day traders make money by doing many small trades over the course of the day. Trading does come with a lot of risk but can also be a very fruitful way to make money.
A popular exchange where people trade is Poloniex.
Trading is similar to listing lots of auctions - the highest buy price wins and adversely, the lowest sell price wins.
One nice thing about trading is that you physically do not need to go out and find a customer to buy the coins you are trading - you simply list at the price you wish to sell at and if the price is right, a buyer will snatch them up. The same goes for buying - you set your purchase price and list your order, when a seller comes along that likes your price, he will accept your "bid" and the coins are transferred to you.
The trick to trading is to know when to buy and when to sell.
Arbitrage
Arbitrage involves buying a cryptocurrency at one price and then transferring over to another exchange and selling it for a higher price. Often, the various exchanges will have a marginal difference in price and after the transfer, buy and sell fees are taken into consideration - it may be very possible to make a profit between exchanges.
Arbitrage involves a certain amount of risk because it may take 10 - 20 minutes to transfer from one exchange to another, during which time the price can fluctuate rapidly, negating the profit on your arbitrage.
This is covered in detail in the arbitrage section.
Lending
Lending bitcoin is a low risk way of making money using cryptocurrencies. Poloniex allows margin trading where people borrow a stock or cryptocurrency in order to trade. In order to do this, they need to fund a margin account which will be used as collateral to cover what they have borrowed as well as to pay the interest on what they have borrowed.
Poloniex allows people with cryptocurrencies to list what they have for lending and select a lending rate. The norm for bitcoin is anywhere between 0.05% and 0.5% per day. Over time, someone can start with just a little bit of bitcoin and continue to compound it to grow it. The risk involved with Lending on poloniex is extremely low because the margin accounts need to be funded before a person can borrow, thereby protecting the lender's bitcoin but the reward is extremely low too.
There are other online websites that offer the same thing, often at higher interest rates. The downside to most, if not all, of these websites is that there is very little that can be done about scammers running off with your coins because there is no forced requirement to have anything in place that protects the lender. No capital, collateral or escrow. I would advise very strongly against using these sort of websites solely on the basis that if someone runs off with your coins, you have very little recourse.
The most profitable way to make money is through day trading.