Uploading video to stream.nyu.edu is a piece of cake!
Just follow the instructions on either the NYU Wiki or the Syllabus site.
From the wiki entry you can upload up to 2 Gigabytes at a time while on campus. From off site they recommend limiting uploads to 500 MB due to speed of transfer and possible dropping of the connection.
Once you have your video uploaded, embed the URL (Uniform Resource Locator) of your file from stream into your word press page. Again you have instructions on the NYU Wiki or the Syllabus site.
Using stream.nyu.edu to upload your videos and embedding them so that they are viewable as movies in your class website is a requirement: work which is not presented as described will not be viewed or graded.