If you use gmail, you can save messages in folders. The folders you have are shown down the left hand side of the page; you will have at least: Inbox, Sent Mail, Spam.
When you are reading an email, you see the icons across the top of the page, like this:
If you click on the 5th icon from the right, which looks like a folder, a window opens with a list of available folders that you can move the email into. Google, rather confusingly, refers to them as “labels”. Click on the folder you want, and the emails will be filed there.
If you want to create a new folder, at the bottom of the window it says Create New. Click on that, give the folder a name, in the box under where it ways Please Enter a New Label Name, and then click Create. The new folder will be created, and your email moved into it.
If you are looking at your inbox, and you can see several emails that could be saved into a folder, click into the box to the left of each email you want to move (the box will get a tick in it). You can then move them to a folder all at the same time, by clicking on the folder icon as above.