Online course on Plant Taxonomy and Physiology
Well, I wasn't able to find an online video course. The closest I came was this site, which links to courses that put their material online. Most of these are compilations of the lecture notes. There's also this page from the University of British Columbia, that has a nice little overview of the field of plant taxonomy.

In my experience, botany and plant identification are subjects where one really needs to learn by doing. You really need to grab a plant and take a close look at it while noting why its in the group that its in. A great way to get started might be to join a local gardening club or native plant society. The people in those groups can provide their tips for ID-ing plants.

One of the primary skills you'll want to learn is identifying what family a plant is in. Plant families have (mostly) consistent characters, and learning how to spot the most common families in your area will be a big help.