First, chemists and molecular biologists create new particles by taking old particles that we already know of and building composite particles from them.
Second, physicists, such as those at the Large Hadron Collider, can drive particles into one another with varying force, and potentially find a new particle from the underlying quantum fields.
And finally, particles that we already know of, can be put into new environments to see how they might react differently or put themselves together in new ways.
Physicists can then see if new particles emerge based on their collective quantum interaction. For more on discovering weird new particles, including excellent demonstrations using Lego, take a look at this video from Minute Physics.
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