Although transferring layers from ArcGIS Online to ArcMap is really easy, the opposite requires a little bit of work if you don't have an enterprise account (which we don't have at UNLV).
Instead, you will need to manually create a ZIP folder for each layer and then upload each ZIP folder into ArcGIS Online.
Why would you want to do that?
Because you may not have access to an ArcMap license on your personal computer, but you have access to a licensed ArcMap in the Lied Library. So you may work for a few hours in the library and then export the layers so you can view and use them at ArcGIS Online (which is free!) at home
Another option is that you created some changes to the data or layers in ArcMap and want to add just that one edited layer back into ArcGIS Online.
Additionally, you may want to export layers for use in ArcGIS Online so you'd be able to use ESRI Explorer app.
Open the folder in which you saved all the shapefiles for this project.
Select all the files related to a specific layer - for example, all the layers named "SewerManholes_C_Buffer_Charleston". There should be around 8 files with different file extensions (suffix).
Right click on your selection, then Send to --> Compressed (Zipped) folder
Windows will create a zip file under the same name as your layer.
Open ArcGIS Online and log in.
You can add this layer to a new map or to an existing map - the process is exactly the same.
Click on Add --> Add Layer from File
In the new window, click on the Choose File button to navigate to the zip folder you created in the previous step.
Now the Charleston buffer layer is added to your map.
Now you can:
This is what the map looks like when the buffer is changed to a light blue color with 25% transparency and is ordered as the lowest layer above the base layers: