There are special websites, mobile apps and other services like ICO Market which publish the schedule of current and coming ICOs. One can study the information and choose a project.
It is possible to buy tokens directly on the website of the project. A bitcoin or ethereum wallet is necessary, or with any other cryptocurrency, depending on a project itself. If a project is implemented on the Ethereum blockchain platform — ethereum currency is needed.
It is also possible to entrust the money to the crypto fund. The analysts of the fund will choose the project and make an investment. Though it is not free: the fund will take a commission for deposits and withdraws; it will also take the revenue share.
One of the ways to create a wallet is to register on a website like Blockchain.info or MyEtherWallet - just follow the instructions. Then it is necessary to deposit to this wallet. It’s preferable to add cryptocurrency accepted by the project.
The cryptocurrency can be bought for fiat money on any crypto stock exchange. The same way the cryptocurrency can be exchanged to another one.
There is a step-by-step instruction on buying the tokens on almost every project website. Mostly, it is enough to copy the number of the smart contract to the wallet and send money. After that, the appropriate amount of tokens will appear in the wallet.
The tokens are traded at the crypto stock exchanges after the ICO is over.