If you are using an APS-C body (with 1.5x or 1.6 FOV factor), then a screw-in 77mm lens hood for a 300mm lens in 35mm full-format will be about the right length for maximum sun shading effect; but be warned--when used on a full-format digital, like a Canon 5D, that length and diameter of lens hood will almost assuredly vignette!
One of the finest lens hoods for a 70-200 on a crop-sensor camera is the Mamiya RB 360mm lens shade, in flexible rubber...it is a simply amazing thread-in shade on a 1.5x or 1.6x body when used with the Nikon or Canon 70-200 lenses...the flexible shade makes it possible to "squish down" the hood a bit when shooting right toward bright light sources, to literally throw a shadow on the front element. I LOVE the Maimiya RB 360 lens shade!!!
Again: the "proper" shade length is determined by the effective angle of view of the lens, which is different if the sensor crops off the outer part of what the lens sees! Which is why a "300mm lens shade" can often be used on a 70-200 lens on an APS-C body. There are a lot of generic, screw-in shades that have been made over the years.