Geting Started in Astronomy Research
Undergraduates do not have the background or expertise to understand the vast majority of existing research, nor the ability to develop a new compelling publishable tractable research project of the correct scope. Therefore, if you are an undergradaute interested in astronomy research, you should seek out a research advisor. At most institutions, there is no formal process for connecting with an astronomy researcher, so most research collaborations begin with the student sending the advisor an email.
This requires knowing which advisors are doing research you are interested in. While the best way to determine this is to read recent publications, this is not practically accessable to undergraduates. An acceptable substitute is to peruse the webpages of possible research advisors (which is, for undergraduates, typically faculty or staff at their university) to find out what they are working on. Of course, there are more personal methods (like working with someone you've taken a class from or going to a research fair or many other possibilites), but these are not required.
What are you looking for in a good advisor and project? Good advisors should be supportive and willing to work with you. For undergraduates, good projects are based primarily on skills that you learn and NOT on the topic. So if you really want to work on galaxies, you can wait to do that when you get into grad school and take the more-convenient-for-now paying internship with that great professor who welcomes you into her group and teaches you computational skills. Another way of saying this is that it is actually rare to work on the same thing in graduate school as you did as an undergraduate. It then follows that
What goes into this email? For a first email, keep it brief. Introduce yourself, express your interest in working on research, and ask if they have any positions in their research group. They might say "no" for a variety of reasons, many of which are not related to you. If you get a "no", don't worry about it and try again with someone else. They might say "you need to take class X, Y, and Z first" and then you'll know which classes are important. Or they might start a longer conversation via email and/or in person. Be persistent and polite. Ideally, they would give you project options and explain the pros and cons of each; don't forget to focus on skills. If they only give you one option that you don't like, ask if you can modify it. Their job is to mentor you well, so don't worry about asking them to shift a project to include more statistics or less observing time or whatever will really benefit you. That said, the best research experiences are mutually beneficial, so recognize that you may need to do some things to help out your advisor from time to time.
Begin as early as possible. If you might be interested in graduate school or if you think research will be a major part of your career, then you'll want as much experience as you can get. Practically every post-graduate trajectory would benefit from research: grad schools want to see research experience since that's what you'll be doing most of the time but employers are also looking for students who have demonstrated that they can solve complex open-ended problems. Some faculty can work with first-year students (or even high school students). Some faculty can pay you to do research, allowing you to get a job and gain experience simultaneously. Most undergraduate research projects, especially early on, are not binding and you can change advisors and/or projects as you go.
There is a wide range of different amounts of time expected on undergraduate projects. During the summer you can work full time. During the semester you might work for research credits. To really make progress, you usually need a relatively consistent 3+ hours/week, otherwise you spend most of your time reminding yourself of what you did last week (or month).