The main technique today for creating these elements is to fuse together two smaller nuclei (of certain sizes, take carbon-12 for example). To be more detailed, you accelerate ions of the two particular isotopes at each other in those cyclotrons, etc. and hope that the extra kinetic energy in a collision will trigger their fusion.
I also seem to recollect firing small particles at some heavy elements works. Neutrons, protons, helium nuclei... this one you might want to check.