Mining Bitcoin is the process of updating the Bitcoin transaction ledger, known as the blockchain. This is done using powerful computers called ASICs, which compete against other miners in an attempt to guess a specific number. The block of transactions, along with the solution, is sent to the entire network so that other computers can validate it. Satoshi Nakamoto and his friend Hal Finney were two of the only people who were mining Bitcoin at that time with their own personal computers.
FPGA (Field Programmable Gate Array) is a piece of hardware that can be connected to a computer to execute a series of calculations. When bitcoins are exchanged, computers around the world try to complete a calculation that creates a 64-digit hexadecimal number, or hash, for that bitcoin. Cloud mining means that you don't buy a physical mining rig, but instead rent computing power from a mining company and get paid based on how much mining energy you have. Chia requires farmers to allocate space on a computer's hard drive, called parcels, to be used by the blockchain depending on certain factors.
Back then, miners only used regular computers, as a standard multi-core CPU was enough to produce 50 bitcoins per block. If you have enough computing power and the cost and availability of electrical energy are not an issue for you, you can choose to mine bitcoins on your own. Each computer that validates your solution updates its copy of the Bitcoin transaction ledger with the transactions you decide to include in the block. Therefore, mining bitcoins requires highly efficient hardware that can perform billions of calculations with as little electrical energy as possible.
Mining groups combine the collective computing power of their members and divide profits based on the proportion of energy each miner provides. It's a basic computer with multiple graphics cards (GPUs) instead of the standard single card, and it does the work necessary to complete a calculation. Instead of computers trying to solve calculations (known as a proof-of-work protocol), computers are randomly selected to create blocks for the blockchain, while computers that were not selected will validate the blocks created. Remember that mining is possible with any old computer, but it's not worth the energy wasted on it because the slower the computer, the lower the chances of getting some kind of reward.