If you have a LETNET account, you already have a YouTube account. Simply sign in with you LETU email and password, then click create a video or post and then upload video.
After clicking this button, it will ask you to upload a video, drag and drop your video or browse to the video to upload.
After selecting the video it will prompt you to enter the video name and privacy settings.
If you set it to Public, anyone can search for it and find it on YouTube.
If you set it to unlisted, you need to send the link to people for them to find it. This is most likely what you want for an assignment.
If you set it to private, then you need to individually grant access to each person that watches it.
After that, you can send the link of the video to you professor through Canvas or however they want it turned in!