I noticed several of these portable plant screens used at the Sunset Magazine gardens to screen or block off certain areas.
This could not be easier: an inexpensive trellis from the nursery or garden center, vine, container, and maybe even a plant stand with wheels. I don’t normally like plastic pots, but in this case I’d recommend a plastic pot that looks like terra cotta because it will be easier to move around and you won’t have to water it as often. Depending on which vine you choose, you might need to tie it to the trellis.
I’d probably do something fairly indestructible like a Jasmine, Bower Jasmine, or Ceanothus because I know I can grow those in a container without killing them. Clematis and Mandevilla are awfully tempting, but I’d probably forget to water them. I believe that’s an Akebia in the picture.
Sunset has a great list of fast growing vines like Thumbergia and Morning Glory that work well in containers.