My (flawed and amateur) understanding is that they create new elements by smashing together atoms on particle accelerators to see if their nuclei stick. If you can create an atom with a new number of protons in its nucleus, in a manner which can be repeated, then you have created a new element.

The last new element that was created with a natural process was found sometime in the 1930s. Many of the artificially generated elements are extremely unstable. Our labs may be the only place in the universe they are made, that aren’t inside stars.