There are lots of guides explaining Mastodon and the broader fediverse, but they often go into way too much detail. So I've written this guide - it only talks about the basics you need to know to start using it, and you can then gradually learn the rest from other helpful fediverse users. Let's get started!
The fediverse is very different from Twitter, and that is by design. It's made for building close communities, not for building a "global town square" or as a megaphone for celebrities. That means many things will work differently from what you're used to. Give it some time, and ask around on the fediverse if you're not sure why something works how it does! People are usually happy to explain, as long as it's a genuine question. Some of the details are explained in this article, but it's not required reading.
The most important takeaway is the "community" part. Clout-chasing and dunking are strongly frowned upon in the fediverse. People expect you to talk to others like they're real human beings, and they will do the same for you.
"The fediverse" is a name for the thousands of servers that connect together to form a big "federated" social network. Every server is its own community with its own people and "vibe", but you can talk to people in other communities as well. Different servers also run different software with different features, and Mastodon is the most well-known option - but you can also talk to servers using different fediverse software, like Misskey.
Like I said, different servers have different communities. But don't get stuck on picking one - you can always move to a different server later, and your follows will move with you. Just pick the first server from https://joinmastodon.org/servers that looks good to you. In the long run, you'll probably want to use a smaller server with a closer community, but again it's okay if you start out on a big server first. Other people on your server can help you find a better option later on!
Also keep in mind that the fediverse is run by volunteers; if you run into issues with your server, then you can usually just talk to the admin to get them resolved. It's not like a faceless corporation where you get bounced from department to department!
It's a good idea to avoid mastodon.social and mastodon.online - they have long-standing moderation issues, and are frequently overloaded.
There are two important parts of the culture on the fediverse that you might not be used; content warnings, and image alt texts. You should always give images a useful descriptive alt text (though it doesn't have to be detailed!), so that the many blind and vision-impaired users in the fediverse can also understand them. They can also help for people to understand jokes that they otherwise wouldn't get. Many people will never "boost" (basically retweet) images that don't have an alt text.
Content warnings are a bit subtler, but also very important. There is a strong culture of using content warnings on the fediverse, and so when in doubt, you should err on the side of using them. Because they are so widespread, people are used to them - you don't need to worry that people won't read things behind a CW. CW rules vary across communities, but you should at least put a CW on posts about violence, politics, sexuality, heavy topics, meta stuff about Twitter or the fediverse, and anything that's currently a "hot topic" that everybody seems to be talking about.
This helps people keep control over what they see, and stops people from getting overwhelmed, like you've probably seen (or felt) happen a lot on Twitter. Replies automatically get the same CW, so it's pretty easy to use.
The fediverse isn't built around algorithmic feeds like Twitter is, so by default you won't really find much happening - what you see is entirely determined by who you follow, and it'll take some time to find people you like. This is normal! Things will get much more lively once you're following and interacting with a few people. Likewise, there's no "one big network" - you'll have a different 'view of the network' from every server, because communities tend to be tight-knit. This also means that it's difficult for unpleasant people to find you.
It's a good idea to make an introduction post, tagged with the #introduction hashtag, and hashtags for any of the other topics you're interested in. Posts on the fediverse can only be found by their hashtag, so they're important to use if you want people to find you. Likewise, you can search for hashtags to find interesting people.
That's pretty much it! You'll find many more useful tips on the fediverse itself, under the #FediTips hashtag. Take your time, explore, get used to how everything works, learn about the local culture, and ask for help in a post if you can't figure something out! There are many people who will be happy to help you out.