This probably doesn't apply in your case, but I was also going crazy trying to figure this out. Everyone was talking about gallery this and gallery that. I even saw Youtube videos showing people manipulating these galleries. And I never got a gallery tab anywhere. I had no idea what was going on.
However, then someone said that you had to save a post before it would work. I had been doing all my texting with new posts that I hadn't saved or published. Once I saved and published a test post and then uploaded images to it, I suddenly got this gallery tab. So that solved part of they mystery for me.
I have to say though, that I still don't understand the logic of how WordPress deals with images. It seems like it should be straightforward, but I get more confused the more I try to figure it out.
For example, I successfuly made a gallery in my test post and I had two images in that gallery which I had just uploaded from my computer. But for the life of me, I can't figure out how to add MORE images to that gallery from my Media Library. It seems that you should be able to just select some files from your Media Library and add them to a Gallery. But I can't see how to do that.
Also, I don't quite understand how these galleries exist without names. Aren't they like groups of pictures or albums of pictures? It makes sense that we should be able to name them and save them and then insert them into different posts.
However, none of these things that it feels natural to do, I can't figure out how to do. And I can't figure out if that means it can't be done or I'm just going about it the wrong way. I'm hoping it will all become clear through trial and error. No matter how many Help sections I read, nothing makes much sense.