Openings for graduate students, postdocs, and scientific staff occur aperiodically. You are encouraged to inquire directly with the relevant faculty member. See the faculty listing for email addresses, etc.
There are also a number of competitive postdoctoral fellowship programs:
An additional list of opportunities can be found on David Hsieh's Lab website: hsiehlab.caltech.edu/opportunities.html
In addition, there are often research opportunities for undergraduates. See, for example, Caltech's SURF program: https://sfp.caltech.edu/programs/surf