A lens hood is a shade that blocks out-of-frame light from reflecting off of the internals within the lens. This minimizes lens flares, so you can add them later in post. Just kidding.
Another form of lens flare is less obvious (and I don’t think J.J. Abrams uses it). It manifests as a haze across the majority of the frame making the image appear washed-out, and it never looks good. Unlike deliberate lens flares, it’s not obvious in the image itself where it comes from and doesn’t look dramatic.
To get the most effect from a lens hood, it needs to block out as much unwanted light as possible without actually showing up in the frame. This means that for any given lens at a certain focal length and field of view there will be a best angle for your lens hood.
The wikipedia article for angle of view gives an equation depending on the focal length and sensor size.
The variable is the dimension of interest. For a lens hood with a simple circular cross section throughout the longest dimension should be used, e.g. the diagonal length of a typical rectilinear sensor. The doubling factor can be omitted if you want to work the angle in relation to the optical axis, rather than the total angle.
The lens hood below is a general purpose lens hood (also 3D printed) for lenses with a 58mm filter thread diameter. It flares out a bit, and the angle is wide enough to use with a ~27mm focal length lens.
The images below show essentially the same 58mm diameter lens hood optimized for 16mm, 35mm, and 50mm, in order from left to right. The length of the hood in each case is 16mm. The shorter the focal length of the lens (and the larger the image sensor) the wider the angle, and the lens hood angle increases accordingly.
So far, I have printed the general purpose lens hood, which errs on the side of wide-angle caution. Once I have the additional test pieces in hand, we’ll give ’em the old Pepsi challenge.