The following is a list of recommended free online videos that cover relevant topics in SharePoint 2013.
Libraries & Lists
Working With Libraries and Lists
Overview of working with libraries and lists.
Creating a Library
Guide to creating a document library.
Working with document versions
Overview of what versioning is and how to use versioning.
Site Contents
Navigating SharePoint 2013
Overview of SharePoint 2013 sites with emphasis on navigation, e.g. top link, quick launch, search, help, etc.
Adding Content to a Site
Using Site Settings to add site content, e.g. look & feel and navigation.
More Options for Adding Content to a Site
Using Add an App to add site content to a site e.g. Announcements added as a web part.
Spreadsheets
Importing Excel Spreadsheets
Instructions on how to import Excel spreadsheets into SharePoint 2013 using Add an App.
Team Sites
Exploring Team Sites
TrainSignal's first look at SharePoint 2013's team sites.
Creating tasks in Team Sites
TrainSignal shows how to create tasks in SharePoint 2013.
Working with features for Team Site
TrainSignal's complete overview of team sites and the features you can use in SharePoint 2013.