The National Science Foundation provides support for undergraduate research at many institutions across the country. At their site, you can see a list of supported programs for 2019. There is a great variety of programs in all sorts of areas, from imaging and computation, solar and stellar physics, planetary sciences, to extragalactic astronomy and cosmology.
Undergraduate research is increasingly a must-have for graduate school, and many employers in STEM fields or the data sciences want you to have a solid research-oriented internship.
Please carefully check out the various programs before applying to see any eligibility criteria, what materials are required, and (above all) when the application deadlines are! (Some of these are pretty soon….)
These are typically highly competitive programs, but don’t talk yourself out of applying. Most places look for people from all sorts of backgrounds and experience, and don’t just rank people by GPA. And somebody has to give you your first chance!
I would be very happy to use the comment thread on this post for people to ask questions about application strategies, how to write a good application letter, how to select people to write letters of reference. I have lots of opinions (and experience!) about those matters, but I would rather the discussion be student-driven than to come down to you from on high.
In case you missed it, Astronomy recently announced the competition for our summer research program.