I have been invited to review a manuscript for a peer-reviewed journal. Actually, this is my first invitation and I am a bit confused whether I should accept or decline. The subject is in the field of experimental physics which is quite different from my research field which is computational physics. In addition, the subject is also different from my background. I really appreciate any advice on this matter and if anyone can guide me whether I should accept or not and why. Thanks a lot for your help and for your prompt reply.
The Committee on Publication Ethics have a nice flowchart for this to walk you through what to consider when asked to review.
When I am asked to review a manuscript I ask myself three questions:
Do I have the time at the moment to do this?
Normally the invitation to review comes with a time limit. In my field this is typically months in the future but can be limited to weeks. If I have a big deadline or other personal commitment coming up I might pass over the review.
Am I qualified to do the review?
When you are asked to review a paper you are often shown the title and maybe abstract too. The job of a reviewer can be broadly thought of as trying to improve a paper. Even if you are inexperienced you might have other expertise which would add something. If the paper is too far away from your field it may take a very long time for you to read and understand which isn't good for you or the authors.
Am I interested in the paper?
Reviewing should be a two way street. In effect you are giving your time away for free! Normally there is an implicit understanding the others will give their time for free to read your work in the future so it all plays out fair. Having said that if you are giving your time away you might want to get more out of the task than simply paying your service. I normally interpret this question in a quite friendly way and have never turned down a review for this reason.
If you have answered yes to all three there is no harm in accepting. Your review is a recommendation that the editor may or may not listen too when making a final judgement. There will also be other reviewers. Reviewing isn't something you should take too seriously and should hopefully something you enjoy doing!
@tr1987 provides a good, general answer. Since you say that this is your first review, and another question of yours suggests you might be early in your PhD, I'd like to add a few points.
You can ask your advisor for advice.
Reviewing is a skill (maybe an art!), and who's better placed to help you get started? Now, there is some field dependence in what's considered acceptable. Asking about general advice in abstract terms should be fine in all fields, but in physics it's usually also OK to discuss specifics about the paper with others. E.g. the report submission form for the Physical Review journals asks whether you prepared the review on your own, or if you discussed the papers with others. (For other journals, asking the editor for permission first would be the safe approach.) Since you're on the fence, asking your advisor whether they think you're qualified to review this particular paper might be useful.
Read the referral from the editor carefully, and have a quick first read of the paper.
Often you're qualified to review part of a manuscript, but not all of it. The editor might know this already, and is maybe looking for a review focusing on those specific parts. Other times they might not be sure what your expertise is (relatively likely if it's your first review), and you should set this straight right away: "I can handle this part, but other reviewers would need to address XYZ". For example, an experimental paper might contain some computations as supporting evidence, which you might be qualified to review, while other reviewers might focus more on the experimental details.
Finally, it's quite common to be asked to review papers about related topics. E.g. as a computationalist, you might be asked to review experiments on systems related to ones you've studied previously, or theoretical papers using methods related to what you've used yourself. If the topic is completely unrelated to your past work, chances are that you're not qualified. However, sometimes system/method A and B have more in common than the names suggest. Learning about such connections and getting a broader view is a very valuable aspect to reviewing.