Ether coins are created through a process called mining. It is done by solving resource-intensive problems using computer hardware, without any central entity monitoring this process.
Every 13.2 seconds (on average), a new block is added to the Ethereum blockchain, which is done by calculating the address of the new block. Each network node tries to find this address, and the first one to do so successfully is awarded with ETH coins.
Since this process can be very random and unpredictable, many users group together in mining pools in order to work together and make their earnings more predictable.
Mining Ether can be done using consumer hardware, most commonly GPUs, so going into this business with smaller investments is certainly possible. However, these machines usually require a lot of electrical power, making such mining a bad choice in countries where electricity is expensive.
Apart from consumer electronics, there are specific devices, called ASIC miners, which are much more efficient at mining cryptocurrency than consumer-grade computer hardware. While ASIC miners are much more expensive to obtain, they also offer significantly higher profit margins for miners.