Before enetering this evasive topic, one must understand what is the difference between species, and strains. Spcies is a name of organisms, similair by nature, and may some subtle differences.  For example, Homospanias (the modern men), is a species. In this species we have some "strains" - black people, white people, tall people, short people, blond people, red-hair people, and so on. This "strains" are actually the same species with a few differences in the gene pool. The same works for mushrooms.
Psilocybe Cubensis is a species, while B+, Matias Romero, A etc, are strains of that species.
Now, that this is cleared we can move on -

Hybrids

*.In theory

Hybrids are strains and/or species created by two (or more) different strains/species connecting between them instead among themselves. This way, a new strain/species is created with attributes from the "parent" sources. You can see a lot of hybrids in the different kinds of weeds. You sometimes see canabis hybrids such as "Skunk X Shiva", "Afghani X Skunk" and so on. This hybrids were created by fruiting one strain with another, and using the seeds, which hold the genetic information of both strain.
In mushrooms, instrain (strains of the same species) hybrids are created by letting monokariotic (each cell contains one nuclein) mycelia from different strain connect between them and creat dikariotic (each cell contains two nuclein) myclia. This way the nuclein of the two strain a presetn in each cell, and you have a hybrid.
Inspecies (between different species) hybrids are generally muatations and will be talked about in the mutations section.

*.In practice

The procedure of hybridizing sounds fairly easy, but without the proper equipment it is based on luck.
1. The most easiet way of creating an hybrid iss by using spores of different strains on the same medium.
     For example, inject spores of Psi. cubensis var. Amazonian and Psi. cubensis var. Thailand, into the
     same jar. Or putting spores of each strain on agar, very close to each other.
     This way there are 3 options :
       A. One strain will overrun the other.
       B. The strain will hybridize and creat a new strain.
       C. The strains will kill each other during their fight for control over the medium (very unlikely to happen).
     This method is based on pure luck and is not very effective, but can sometimes work.
2. The "scientific way". This way you must have a very sterile enviroment, a microscope, and an inoculation
     needle. What one must do is - Take spores of two different strains, and germinate them on seperate agar
     plates. As soon as they germinate, take them into the sterile work area, and put one plate under the scope.
     Isolate one monokariotic cell, and place it on a new clean sterile plate (with no agar inside). Take the
     other plate (containing another strain), place it under the scope, and take one monokariotic cell. Place it
     on the plate with the other strain's cell. Make sure both cells are touching each other. Now wait. When
     you that dikariotic cell is formed, immediatly transfer it to a new agar plate(with agar in it). This cell is
     actually a new strain. You should wait until it grows on the plate, then use it as you wish (continue another
     generation on agar, use it to colonize spawn, or whatever.
 

*.In Conclusion

There are two major methods used to hybridize. One for the home cultivator, and one for the proffesional mycologist. Both can work.
Not all hybrids, will nesscerally be better then the parent strains, because the new strain will contain a mixture of the genetic information from the parent strains. With hard work and persistency, one could creat good strains, if one so wishes.
 

MMA wishes to thank Trade_Omlet for this contibution.