Atoms are split not by lasers or whatnot, but split by themselves.
Lets consider Uranium-235, the main component in nuclear fission reactors. The Uranium-235 has 235 neutrons in it. Neutrons are then "shot" into the Uranium-235, and when it hits the atom, it adds itself to the 235 neutrons.
This turns the Uranium-235 into Uranium-236, which is highly unstable.
The atom oscillates, and eventually "splits" in two.
One possibility is it splitting into Krypton-92, Barium-141, and three Neutrons. The 3 Neutrons go out and mesh with other Uranium-235 atoms and cause a chain reaction.
Another way to split atoms is by using a particle accelerator.
A particle accelerator uses a very strong electromagnetic field to propel charged particles.
By having subatomic particles impact other particles at near-light speed, scientists can split atoms into their fundamental components, essentially destroying them to study them.
That's why these accelerators are called "atom smashers" in pop culture.