For the bitcoin timestamp network, a valid proof of work is found by incrementing a nonce until a value is found that gives the block's hash the required number of leading zero bits. Once the hashing has produced a valid result, the block cannot be changed without redoing the work. As later blocks are chained after it, the work to change the block would include redoing the work for each subsequent block.
Because it's similar to gold mining in that the bitcoins exist in the protocol's design (just as the gold exists underground), but they haven't been brought out into the light yet (just as the gold hasn't yet been dug up). The bitcoin protocol stipulates that 21 million bitcoins will exist at some point. What "miners" do is bring them out into the light, a few at a time.
The receiver of the first bitcoin transaction was cypherpunk Hal Finney, who created the first reusable proof-of-work system (RPOW) in 2004. Finney downloaded the bitcoin software on its release date, and on 12 January 2009 received ten bitcoins from Nakamoto. Other early cypherpunk supporters were creators of bitcoin predecessors: Wei Dai, creator of b-money, and Nick Szabo, creator of bit gold. In 2010, the first known commercial transaction using bitcoin occurred when programmer Laszlo Hanyecz bought two Papa John's pizzas for 10,000 bitcoin.