Getting Started!
Welcome to your new Linux machine! Usually, your computer will present a welcome guide on its first startup, telling you about some important features, things to check and adjust to your liking, and links to resources. Look over that welcome screen, follow its instructions if it has any, and go over the key things that it recommends.
If you're using Linux Mint or Debian, make sure to get your firewall going! It is turned off by default at first. Mint warns you about it, while Debian expects users to have that on their own priority list.
Go ahead and check for updates before you go further. Those will be in different places depending on the desktop environment.
If you are on a flagship desktop environment (KDE/Gnome/Cinnamon/COSMIC), you will have a software application. GNOME calls it Software and KDE calls it Discover, while Linux Mint splits its Software Center and Update Center into separate things. It's a mixed bag with Xfce and other lightweight desktops, depending on the distro. Ubuntu is far-and-away the easiest, with an App Center shared between its flagship release and all the smaller spinoffs.
After you run those updates, it may tell you to restart. Restart the system and you're good to go!
Okay, now what?
Use your computer! surf the web, watch a video, mess with a paint program, install Steam and play some games. Whatever you would normally do with your computer before, try it on your new Linux machine!
Take some time to look through the software library. Think about the things you'd like to do, and see if there's something for it. Interested in 3D modeling and animation? Install Blender! Wanting to try some digital art? Try GIMP or Krita! Need some ambiance? There are apps for playing ambient sounds, or even hourly Animal Crossing themes.
Give yourself a few days to just soak it in and use it. If you get curious, look into customization. Change up the cursor, icons, accent colors, wallpaper, whatever else to make it feel like home.
Once you feel comfortable using your machine, try and carve out a little time to learn about how it works. I will provide some basics in the following sections, but it'll be far from exhaustive.