How are anti-matter atoms created? What is the reaction, or reactions that make anti-matter? I don't understand how anti-matter is created by CERN if interaction with normal matter causes annihilation. 
 A: Anti-matter is created from interactions. They are created as a way to conserve energy and other quantum numbers such as charge. One such interaction would be the $Z^0$ decay:
$Z^0 → ν_e + \bar{ν_e}$
In this case lepton number is conserved.
They do annihilate producing energy (usually photons, but they can produce other particle-antiparticle pairs) when they interact/collide with their own antiparticle. They are produced in really low amounts therefore the annihilation is not as destructive as one might think from reading pop science.
A: For over forty years accelerator technology has been giving antiproton and positron beams, the easiest to create anti particles.
Positrons are the simplest because once the energy of electrons is accelerated to the values over pair creation of e+e-, the the brehmstrahlung photons, gamma ray energies, will create electron positron pairs when interacting with the field of target atoms, and the positrons can be lead with magnetic fields into beams.
Antiprotons are harder to create because a proton antiproton pair needs energies over the 2 GeV necessary for the rest mass of the baryon antibaryon pair. Antiprotons are created by accelerating protons to high enough energies hitting a target and generating a plethora of particles through the strong interactions. Among them there will be proton antiproton pairs and the antiprotons will be separated from the rest and guided into a storage and then beam acceleration systems. To create antihydrogen the antiprotons should be low enough energy to be able to capture positrons and create atoms, as described in the link.
