Is there a way for students to upload a video as an assignment? What would be the maximum file size for that video and also what format should the video be in?
You could look at Kaltura that integrates with a plugin to Moodle. We looked at it 18 month ago, but concluded the open source version of the videoserver was too buggy. However the Moodle plugin worked.
At that point it added a video assignment, if you are on a pre 2.3 installation I think that is how it will work.
If you have money you can buy the commercial version of Kultura that I suppose works fine. They have an education license.
A student can upload a video as an assignment with the standard assignment type if you allow file uploading. (They can upload any type of file) The size and file format depend on the teacher really - you can specify in the assignment and in the course settings the max upload size and as for the file type it depends on how you want to view it - it would need to be a format the teacher is able to view on their computer. Other options do indeed include Kaltura -or even getting them to upload their video to youtube and providing the private link in the assignment so the teacher may see it. This gets away from the issues of file type and size.
Basically what Mary just said ...
But I want to elaborate a little. It would help to know what version of Moodle you are using, and how long the videos are, to answer your question.
In Moodle 2.3 the assignment changed and so did some of your options. But simply put, you can offer your students the option to upload a file, as the assignment submission.
If you are uploading videos (ie not shooting them from a webcam) then MP4 is probably the best format. That is because it plays back on most devices and is well supported by online video players. But asking your students to convert their own files might be tricky. So it will probably depend on how you are asking them to record their videos.
File size depends on your server, the distance from your students to the server, and the length of the videos, and how they are recording them. But in general small is good. When shooting from a webcam, I aim to keep file sizes no greater than 1.5M per minute.
Actually I worked with an organisation earlier this year who needed very long video files uploaded as assignment submissions. We made a Youtube assignment submission type. The plan is to release that back to the community. This would clear up the need to worry about file formats or file size.