When I first came to Berkeley, I knew absolutely nothing about research. It can be very disheartening to see people around you come in with research experience and easily get opportunities straight out of high school. I remember feeling like I would never be able to catch up, that no matter how much experience I had, I would always be one step behind those who were just lucky enough to start earlier. Luckily, there are loads of opportunities at Berkeley for students interested in pursuing research - chances are if you are interested in something you will eventually be able to do it. Here are some tips I've picked up on speeding up the process.
Go To Things
If you find a topic interesting, see if you can figure out which labs on Berkeley work in that area. Nearly all labs that I've worked with have a mailing list or website where they send out information about what events are happening. These events include seminars featuring researchers from other universities, talks from graduate students on their current work, and sometimes even socials. At first, don't worry if the technical details fly over your head - focus on grasping the ideas explored in the current state of the art. Look over the work that will be presented before showing up if possible, and write down any questions you have. Asking questions can be nerve-wracking, especially when you aren't sure whether it is a misunderstanding on your part, but having questions prepared alone is a good way to think a little more deeply about what is being presented.
Talk To People
Talk to people. This includes grad students and professors. If you glance over their work on a conceptual level before showing up, you will be able to engage with them on what they are currently working on. If you don't have much experience yet, listening to what grad students are working on is a great way to get insight into how they work and what ideas they find interesting. Don't approach every conversation with the goal of getting research - instead, try to make genuine connections with people and find out who you share interests with. You will be much happier if you don't just jump on the first research opportunity you get.
Don't Be Afraid
As a TA I get at least five emails a week from students. Grad students get more. Professors get much much more. Don't be afraid of emailing people, even if you don't think you are fully qualified. Check their websites to see whether they have any specific requests/requirements, but if that information is not listed there is no harm in reaching out. Either your email will be ignored (it happens a lot) and they will forget your name as soon as the email leaves their sight, or they will be happy you reached out. Even if you aren't at a point where you can work in their lab, they may be able to point you towards resources you can explore to gain experience before trying again. Pre-requisites are there to inform you what level of information you will need to be able to digest to spend a normal amount of time on a class. However, if you are truly passionate about something, don't be afraid to dive in and try it anyway - I ended up taking CS 288 before CS 189 or CS 188, and while the projects took me 5x longer than they took everyone else, I learned a lot and was able to contribute to research earlier in my college career than I otherwise would have.
DARE - Diversifying Access to Research in Engineering, a program that connects students who are underrepresented in academia to professors and graduate students doing research
URAP - Undergraduate Research Apprenticeship Program, for students who are interested in pursuing research in a variety of areas (for CS students, there are a lot of interdisciplinary opportunities)
EECS/CS Honors Program - for students who want to complete an honors thesis
SURF - Summer Undergraduate Research Fellowship, for students who are already involved in research to get funding from Berkeley to spend a summer working exclusively on that work