Your Drive is where you will find all the work you create with Google services, along with files you add. You will also find any of the above that people shared with you.
Because your Drive is the central train station for all your work in Google apps, it can bewilder. You may find it hard to see what is your work, what is someone else's, and who can see what. Leave time to practice and develop your own ways of making sense of it.
Here is a good video introduction to Google Drive. Set aside 20 minutes and watch it.
This cheerful introduction teaches about Team Drives, which are an addition to Google Drive as of 2018.
The two videos above will give you all the background you need.
Where can I find something someone shared with me? You have two ways to find these. One is to click on “Shared With Me,” which shows you all the files people have shared with you, usually sorted with the most recent ones on top. Perhaps a better way is to start typing the name of the person in the Drive search bar near the top of the screen. It will auto-fill with names from our district; click on the one you want. Now you are looking at the files owned by that person.
What does it even mean to add someone else's file to “My Drive?” Usually “My Drive” is full of things you made or put there. You are the owner. But if someone shares something with you, you can choose to add it to “My Drive,” right alongside your stuff. That person will still be the owner, but you can get at it more easily. If they stop sharing it with you, it will disappear.
What does it mean to share something with someone else? For any file or folder of files in your Drive, you can choose to let someone else View, Comment, or Edit your work. View means they can only look at it. Comment means that (for Docs, Sheets, Slides, and a few other things) they can highlight some text and type a comment. Edit means they can do everything to the file, including deleting and renaming it (it is possible to restrict other people from changing the sharing settings).
Is it bad security to share a file with someone? Assuming you share it with the right person, it is actually better security than many other options. For instance, if you add a file as an attachment to an email, you lose control over who gets in next. It could be sent to anyone. In the case of a file in your Google Drive, however, you can always decide who gets to see it. Of course, nothing stops people from taking screenshots or copying and pasting – so don't use the security model as a chance to say potentially damaging things. But overall, it has security settings that are more powerful and fine-grained than others.