We create synthetic elements by smashing together atoms of two different elements at high energies, or by smashing a single atom with some other particle at very high energies. For example, one atom of the element americium can be made by hitting a plutonium atom with a high energy neutron. All of the synthetic elements are radioactive, which means they turn into other kinds of elements. This is why they are not found in nature. For example, each americium atom will decay into one neptunium atom plus one helium atom.

You can create new elements by bombarding them with neutrons and hoping that the neutrons will get absorbed into the nucleus.