Maybe you've heard of people "mining" on blockchains like bitcoin. That is what helps everyone agree. Think of a game where teams try to guess a combination of a lock. The team who guesses the most combinations to the most locks gets to say what the facts are, and gets paid. But there's usually only one team, since everybody wants to be on the winning team. So everybody is helping to guess combinations and get paid. But one person wants to lie and say they spent their money elsewhere. They would have to wait until their first transaction gets confirmed, and their product is in their hands. And then they would have to start guessing more correct combinations than the rest of the world combined, something that is nigh on impossible. But it's not people guessing combinations, it's many computers guessing at millions of times per second to a super-complex combination lock. This uses a lot of power, which is one of the criticisms of the Proof of Work algorithm. This algorithm is used by most prominent cryptocurrencies like Bitcoin, Litecoin, and Ethereum (though ETH wants to switch to PoS).
Imagine there is a group of people who have to agree on a ledger of facts, transactions, etc. But in order to be able to pick a ledger, you have to put $1000 on the table. Now, a series of ledgers are passed around the table for people to sign. If you sign the ledger that the most people sign, you get $10, if you sign a different one, nothing happens. But if you try to sign two or more ledgers, you lose your whole $1000. This makes everyone agree on the one ledger of facts and can continue to sign more ledgers from there. But it's computers with currency on the blockchain that "stake" their currency on a ledger to get paid for it. But this causes people to hoard currency, which is the main criticism of the Proof of Stake algorithm. Notable usages include: Peercoin, Nextcoin, and possibly Ethereum in the future.
The point of this algorithm is just to prevent any one person from spending the same money in 2 places, so we really only need to choose one ledger or another, since the same person can't be on one ledger twice. 80% of the people must agree. Think of it this way, a group of people have 2 doors to walk through. 80% of the people have to walk through the same door or they have to go back and try again. Now, one person could lie and say they walked through both doors, but it would be easy to tell who that was (they voted on a ledger that contained 2 transactions from the same person), and nobody would ever trust them again. Eventually everyone will agree on which door to walk through, making the other door invalid. This sounds a lot like Proof of Stake, but nobody stakes currency. It's a little less secure, but real world data seems to say that it works. In most cases, no currency is generated by the blockchain to pay the confirmers. This is a more technical explanation of how this works: https://www.quora.com/How-does-the-Ripple-consensus-process-work. The most notable user of this algorithm is Ripple, but it is getting more traction as a way to avoid generating new coins on the blockchain.
They get paid money that is generated by the blockchain. Think of when the government prints new money, but instead of keeping it for themselves, they would distribute it to everyone. Or at least, distribute it to the people who keep everyone's transactions safe and secure. For some blockchains, the money is not generated, but included as a fee in each transaction.
This has been Alavan,
Thanks for reading, don't forget to upvote and all that.