A widget is just some computer code that is generated for you (no coding skills required!) which you then copy and paste into the place you want the content to be displayed. That might be inside an LMS like D2L, or in a blog sidebar, as you can see right here at this blog, where I have an #OpenTeachingOU widget.
Twitter widgets are really powerful and flexible because you can create a widget that displays a specific user (which is what you will do if you have a class Twitter account) or a specific user's likes, or a hashtag (like for #OpenTeachingOU in the sidebar of this blog) or any other search result for that matter, or a public list.
Design the widget. To get the Twitter widget code that you need, go to your Settings in the upper-right hand corner, and select widgets, then Create New. You will see an interface to let you choose from all the options and also to preview the results. When you are done, click Create Widget. You can then access this widget configuration again any time in the future either to retrieve the code and use it, or to make changes to your choices.
NEXT STEP => Now that you have a widget ready to use, you can configure your D2L homepage so that your students will see the widget there!
Note: If you are not using D2L or an LMS and instead want to display the widget in the sidebar of a blog, that's easy: just copy the code from the Twitter widget configuration page and paste it into the blog sidebar box (make sure you are pasting into the HTML view of the box if the blog has a WYSIWYG editor). You can also paste in the widget to a wiki or website; you can see my class Twitter stream displayed here in the sidebar of a PBWorks wiki for example: Online Course Lady Wiki.