The parallel view method is easily explained. The left and right images are put horizontally next to each other at a distance of not more than 65mm (which is the average human eye distance). The viewer needs to hold his head exactly vertical and try to look "through" the projection plane as if he was looking at an infinite distant object.

Normally, when doing this for the first time it is hard because the eyes need to focus on some fairly near image while there is no or only little convergence (angle between the left and right eye directions). However, after looking at it for a while, one gets used to it and the images get sharp with fairly well 3d effect.

While it is quite easy to achieve orthostereographic projection using this way, there is little use for the parallel view method since it limits the (horizontal) image size to about 65mm and is best presented on printed paper.

The cross-eyed view method works much like the parallel view method with the left and right images exchanged. Hence, when looking at the images, the viewer must look at the left image with the right eye and vice versa which means that the convergence angle is fairly large. This, in turn, allows to use somewhat larger images (more than 65mm wide).
(Note that you can look cross-eyed at parallel view images when turning the projection plane upside-down.)

As with the parallel view method, when looking at it for the first time, it is hard to get the images sharp because the brain thinks the focus point is much nearer due to the large convergence angle. After some time (contemplate!) one can overcome that.

Note that there is no way to achieve orthostereographic projection using the cross-eyed view method since the eye rays for infinite distant objects cross about half way in front of the projection plane. (In order to correct for that one would have to transform it into a parallel view image.)
The 3d effect is not very well and looking longer at these images is likely to produce eye strain.