SharePoint is a collection of a bunch of List & Libraries. Maybe you have a Team Calendar, Shared Documents Library, Task List, or Discussion Board. All of these list and libraries you can put on your main page of the SharePoint site and arrange the site page anyway you want. To do this, you use something called Web Parts. This guide will help you understand how to use Web Parts.
You will now see your page is in edit mode. You now have a lot of new options to edit the look of your SharePoint page. If you look at the page, you will see it has a layout. You might have one single layout, or you might have a header, and a left and right. The First step in editing your page is to choose your layout. On that edit ribbon, on the right, click Layout and choose what type of layout you want for your page.
Once you get the layout how you want it, its time to start adding web parts. Click into a column on the page and click the Insert tab in the top ribbon.
Once you click the insert tab, you have a bunch of options on what you can insert. On this guide, we are going to talk about Web Parts and App Parts. App Parts are new for SharePoint 2013 but they are just about the same as Web Parts. You can explore the differences at your convenience. Click on Web Part.
As you can see, you will have a lot of options on what you can add to your page. If you have not added the List or Library to your page yet, then you wont see it here. This only picks up content that has already been added. So, For this example, we are going to choose "Documents" and click Add.