Mastodon is a microblogging social media platform similar to Twitter but with a few key differences. Instead of being owned and operated by a company, Mastodon is a collection of servers that are run independently from each other, operated by volunteering members of the community. It's an open platform with no algorithms, no ads and no corporate ownership.
Mastodon works a little like email in the sense that just like picking an email provider (Gmail, Outlook, iCloud, etc.) you need to choose a Mastodon server to register an account on. Once you've joined you don't really have to think about there being different servers because they're all connected to each other. No matter which one you choose you'll be able to interact with and follow users from any other server. It feels less like being on a server and more like using the server to access one big platform. Similarly to email addresses usernames also consist of two parts, your name and the server you're on: @name@servername.
There are a number of furry themed servers run by furry admins. Here is a list of some of the more popular ones (all of these allow NSFW posts):
*meow.social is currently invite-only
If you're looking for a server themed around a specific interest (e.g. macro, inflation, transformation, VR) you can find a more extensive list of servers at furryfediverse.org
Mastodon has no content recommendation algorithm that could decide what it promotes or suppresses. Instead post discovery works organically, driven by using hashtags and 
boosting (reblogging) posts. Hashtags play an important role in finding people posting about topics you're interested in and you can even follow specific hashtags just like following users. Here are some examples of frequently used furry and art related tags:
#Furry #FurryFandom #FurryArt #DigitalArt #MastoArt #FursuitFriday #Raffle #Commission #CommissionsOpen #FurryWriting #FurryMusic
Image descriptions (or "alt text") have two functions: they're what's displayed in case the image itself fails to load and they also provide context for vision impaired users who are relying on screen readers. are short texts for describing what's in an image or even providing additional context. They can make posts easier to find via the search function and they also help users with impaired vision who rely on text-to-speech. It's generally a good idea (and also encouraged by Mastodon's culture) to describe the image in a few sentences in the alt text.
You can also include content warnings which work a bit like the email subject field: an optional, short one-line description. If a post is hidden by a CW the users can choose whether to open it or not so it's useful in case of sensitive topics that not all users might want to see. Posts that have CWs only show that one line by default and the rest of the post can be revealed with a button. Most servers require NSFW topics and images to have CWs. Users can control what they see by setting posts with CWs and NSFW images/videos in their feed to either remain hidden unless opened or be always visible automatically.2
Besides the official Mastodon app there are several third party mobile apps:
Posts on Mastodon can be edited after they are published; you can add tags or even replace images that have errors in them with a fixed versions. You can also set the language of your post and choose to only see posts in certain languages in your feed. The default language for your posts is usually the same as what Mastodon's interface used for you by default so if you're not a native English speaker but post primarily in English, you should set your posting language under Settings > Preferences > Other.