Banking system uses centralized control and transactions (fiat transactions) are handled and validated by banks or financial institutions. Cryptocurrencies, in contrast are decentralized and controlled through a public transaction database called blockchain. Transaction happen peer to peer, means no bank or authority is involved. Transactions are validated by the network through complex mathematical calculations. Everyone in the network can contribute their processing power to this calculation and get cryptocurrencies in return. So mining in cryptocurrency world actually means contributing your processing power for a validation of transactions and coins are rewards that you earn for your contribution. Once mined, these coins can be used and exchanged just like money through a crytocurrency wallet.
Bitcoin invented in 2009 was the first cryptocurrency and has sky rocketed in value recently. Back in the early days it was possible to mine bitcoins from any computer. But today the complexity of the operations and size of the network is such that you need expensive hardware with lot of power consumption to make a worthwhile mining effort.
Many new alternatives to Bitcoins are emerging every day and these are grouped as Altcoins. When a new cryptocurrency launches the size and complexity is such that even normal CPUs or GPUs may be used for mining. However the value of cryptocurrencies are fluctuating all the time and it is harder to predict which one will go up in value. Also the value of the coin may be less than the cost of electricity used to run the processor. As the popularity of the coin rises, solo mining becomes impractical and you may need to join a trusted mining pool and they may charge small fee that adds to your costs.
Some of the popular altcoins that can be mined with CPU (normal processor such)/GPU (graphics processor) are
Monero(XMR) is focused on privacy and one of the top 10 cryptocurrencies by market cap. It can be mined by anyone with a CPU or GPU. The mining app with GUI is available to download for Windows, macOS, Linux, Android, and FreeBSD from official Monero downloads page. You can also download wallets from the official site. It is better to join a mining pool than going solo. GUI mining tools with mining pool selection is offered by third party websites but be sure to verify the sources and do not be tricked into downloading malicious software.
Bytecoin (BCN) can currently be mined using CPU or GPU. To solo mine bytecoins, just download the wallet and daemon from official Bytecoin downloads page. However solo mining is not worth the effort. To pool mine using CPU or GPU you may use one of the Bytecoin recommended mining softwares that also helps you connect to a pool.
The Zcash (ZEC) network is still in early stages and continuously evolving. It offers better privacy using zero knowledge cryptography. It can be mined with CPU or GPU, but GPU mining is more efficient. The official Zcash client is available for Linux, but modified versions for Windows and Mac have been created by the community. You may also run the Linux version on a virtual machine (VM) although this is less efficient. For GPU mining you may use more specialized software As with the other currencies, it is better to join a mining pool for which you require third-party software that you can trust.
AEON is a mobile-friendly currency that offers light-weight transfers. CPU mining is possible. You may download the windows 64 bit zip file for the daemon here. As with others it is better to join a pool than doing it alone.
DigitalNote (XDN) employs secure CPU efficient ASIC(application specific chips) resistant mining. The wallets and software can be found here
FantomCoin (FCN) supports merged mining (simultaneous mining of two cryptocurrencies) with other currencies such as Bytecoin (BCN), Monero (XMR) or QuazarCoin (QCN). Downloads for Linux, Windows, Mac as well as source code are available at official site.
There are many third party mining tools that allows you to mine different currencies and join the corresponding mining pools and also supports merged mining. However be cautious when installing third party miners and always go with softwares that are recommended at the official websites. Even legitimate miners raise alarms from Antivirus softwares, but you could bypass these warning if you are sure the software is not malicious.
Alternative: HD Farming
This article won't be complete without mentioning HD (Hard Drive) mining. In HD mining you contribute hard drive space instead of computing power and this can be done on any normal PC. An example to this is Storj. You can sign up at the Storj official website and rent your hard drive. All you need to do is install the desktop application from the Storj site and configure it. You will get paid in to a wallet of your choice.
Mining is not the only way to get cryptocurrencies. You may either exchange them for cash or other crypto currency at a cryptocurrency exchange. Fiat exchange(exchange for cash) is supported by only some of the currencies but exchange between currencies is easier. Like any other investment, investing in cryptocurrencies carry a fair amount of risk. So choose your investments wisely.