First of all, it’s worth saying that most people do not need to use multiple accounts. The Fediverse is designed in such a way that people on different servers can interact seamlessly, as if they were all on one network. One account lets you interact with people on the whole network.
However, some people may need separate personal and work accounts, or an extra account that focuses on a specialist topic which they wish to keep separate from their main account.
Whatever your reasons, it’s very easy to use multiple accounts on Mastodon and the Fediverse: all you have to do is sign up on a different server for each account you want. Because the servers are independent, you can use the same email address for each account, and you can be signed into all the accounts simultaneously on the web or on an app. Signing up for accounts on different servers also means that if one server goes down you can use your alternative account on another server.
If you use the Fediverse through the web, you can log into all the accounts at once and switch views by keeping each account open in a separate tab.
Official and third party apps support multiple accounts too. You can be signed into all your accounts at once, and switch between them within the app. The interface for switching differs from app to app.
On the official Mastodon app, you can add accounts and switch between them by holding down your profile image in the bottom right corner. A menu will appear which lets you add or switch accounts.