When most people ask this question they are actually asking how to use Ether, the main currency of the Ethereum platform. But the Ethereum platform can be used in many ways as well.
Ethereum is a platform that can be used by developers to create decentralized applications (dapps), tokens/cryptocurrencies, and basically anything else that can be programmed. It was the front-runner of the race to develop what is sometimes called Crypto 2.0: blockchain technologies that go well beyond singular usage as digital currency and instead reach and revolutionize every aspect of digital technology in the world today. People can and do use Ether, the primary currency of the Ethereum system, to make transactions like a currency, or as an investment.
The intended use of Ether was as a token which is the reward for the miners and to pay transaction fees to other involved in the process of powering the Ethereum blockchain. The network itself can facilitate all sorts of processes. While Bitcoin introduced blockchain technology to the world, it was only meant to be a currency. Ethereum is the soil in which new blockchain technologies can grow. The first launch of Ethereum client software in 2015 was called Frontier, and the activity surrounding the platform since that moment has looked a lot like the Gold Rush of the American Frontier days, characterized by excitement, uncertainty, greed, lawlessness, booms, and busts.
Startups with new coins or tokens using the Ethereum system have raised millions of dollars through ICOs (initial coin offerings), but due to a lack of regulation and transparency, many of these have turned out to be scams, unfortunately. Another significant hiccup was the DAO, an ad-hoc venture into decentralized corporate structure and governance that, while promising, ended up being compromised by hackers, who siphoned off millions of dollars worth of Ether and caused the Ethereum community to implement a hard fork.
This should not be taken to mean that Ethereum is a walking disaster; it still appears to be the most elegant and promising platform for this new technology to thrive, and the price of Ether has only recently hit its highest valuation to date, as of the time of this writing. Large companies such as Microsoft, JP Morgan, and others, are using Ethereum protocol as the foundation for their own research and development for permissioned, private blockchains in the corporate and banking world.