Click on the pinwheel Kaltura icon with the tool-tip "Embed Kaltura Media" (see screenshot) in Pages, Announcements, and so on.

This takes you to your My Media account, and you can add videos you've already uploaded, or create and upload videos right then and there.

This method will place videos in context, wherever in the course site you think it is best for students to encounter the media.  You also have the option of adding a Media Gallery to your course space to collect all the videos in one place (Canvas@Illinois , Managing Course Navigation Links ).  You can also add a link to My Media, which will allow instructors and students to access their media from inside Canvas just like they can in mediaspace.illinois.edu.  

Students can add videos, too, wherever they see the text editor, such as on assignments and discussion board posts.

You might need to click on the three dots to expand the toolbar to access the Kaltura button.

Instructors can add a link to a Kaltura video in places in Canvas where you don't have access to Kaltura through the text editor, such as in "New" quizzes.  First, copy the "Link to Media Page" from the Share tab of your video (Kaltura, Obtaining embed code or link for media ), and then use the Insert Link button on the edit bar.  By default, this opens in a new tab.  You'll need to make sure students can view the video in mediaspace.

Instructors, if you want students to submit videos in assignments, you will need to select the Text Entry option when setting up the Assignment.

Here is a video demonstrating the Kaltura Mashup:

https://learning.kaltura.com/media/How+to+Embed+a+Kaltura+Media+in+the+Context+of+a+Canvas+Course/0_4weol2uv