The Ethereum Virtual Machine (EVM) runs smart contract code by reading bytecode instructions one by one. It uses a stack to hold temporary values and memory to store data during execution. For example, PUSH1 adds a value to the stack, MSTORE saves a value from the stack into memory, and CALLVALUE pushes the amount of ether sent with the transaction. The program counter moves through instructions, and JUMPI can jump to a different instruction if a condition on the stack is true. This step-by-step process updates the blockchain state or returns output. The execution table shows how the stack and memory change after each instruction, helping beginners see exactly what happens inside the EVM.