There are two ways to burn money on an Ethereum blockchain. The first way is to accidentially lose a private key or to send money to a contract that cannot be retrived. In this case, total sum of money of all accounts in the blockchain remains unchanged. The second way is to just magically make money disappear. After you do that, the total sum of money of all accounts in the blockchain will be reduced.
In an Ethereum blockchain, to burn money in the second way is really easy using the SUICIDE opcode. The SUICIDE opcode accepts one argument – the receiver of the money to be transferred. It then sets the current account balance to zero. So if one accidentally set the argument as the same account as the current account, the money will first be transferred to itself – no problem, but then, the current account balance – again this is the account itself – will be set to zero. In this way, some money is just burnt to nowhere.