The Beehive application, formerly called ResearchMatch and designed by your own colleagues who are alumni of Prof. Fox’s CS169 course under the guidance of Prof. Jeff Bokor in EE, is designed to make it easy to find listings that match your skills, availability and interests.

There’s also various EECS programs (info TBD).

But before you browse them, here are some tips that should help your search.

The single biggest source of problems in undergraduate research, whether for pay or for credit, is overestimating how much time you’ll have available and/or underestimating the effort required for your courseload or the research project. 

Spending 3 or 4 hours every other week on a project is essentially wasted time—yours and the project’s—and the project leaders won’t be happy about it. Your potential faculty supervisor will likely ask you about your course load.

So, how to maximize my chances of being offered a position?

1. Have a reference or two (graduate student you worked with, supervisor, colleague, etc.) who can attest to your ability and work ethic working on other projects, even if just course projects.
2. If the problem is one of funding, be willing to consider working for credit initially, with the informal agreement that if all goes well you will be first in line when more funding does become available.
3. Don't just show up and say "Do you have anything for me to do?" Learn about the projects people are working on (often their PhD students' home pages are more informative than the faculty home pages or even the group/lab home pages). If they have recent papers that are accessible to you, check them out. Talk to the PhD students. They are on the front lines, and besides describing the project, may also have a better sense of what parts of it could use some extra assistance.
4. Don't spam faculty with identical emails. If you intro yourself by email, do it in a personal way, offer to drop by in person, and provide enough background about yourself and why you're a good candidate that you will in fact be invited to drop by in person.
5. Realize that people are really busy. If you don't get immediate responses, or the responses or short, don't get offended and don't give up. Also remember that faculty plan ahead, so if you want to do research in summer, apply in early spring, and so on.

What skills/courses do I need?

Obviously it depends on the project, but it's good to be comfortable with a variety of languages and frameworks to maximize your appeal to software-intensive projects. Working on extracurricular projects (hackathons, Blueprint, DeCal courses, etc.) or taking high-quality online courses from sites like edX or Coursera is a great way to do this.

Do you take non-Berkeley students as research interns/assistants?

I can sometimes take local (Bay Area) high school students as summer interns if they have the right skills.

Other than that one exception, I cannot take non-Berkeley students as interns, except through organized programs such as SUPERB.