There is no animation whatsoever. It simply flashes onto the screen, remains there for approximately four seconds, and then fades out. Its design is simple, but effective. Taking into account all the marvelous, but instantly forgettable trademark logos, this isn't one of them.
It consists of several seemingly interlinked lines making a square shape with two rounded corners (a blue square, not easy to forget) with the name 'Filmways Home Video' underneath it. These words aren't exactly fancy, and the only difference is the 's' at the end of 'Filmways'. Similar to the 'f' in several flash drives.
The image above that logo (on my last post) is possibly a remade version of the logo to make it seem more modern. However, in my opinion it's too much like the 'Universal' logo. I can't find a video of what that logo looked like when animated however.