[Astronomy] First time peer reviewing

Part of every scientist's job is to contribute to the literature. This responsibility comes in two forms. First, there's writing your own papers, submitting them to journals, and having them be published. With my thesis now fully published, I've got a decent amount of experience at that - four first author papers, and several papers on which I'm a secondary author. Fine.

The second part of the responsibility is that of being the referee (or one of the referees) carrying out peer review on submitted papers. Asking around at work it seems as though quite a few people actually did this for the first time during their PhD, or at least fairly soon after starting their first postdoc position.  I actually had a request last year, but I was in the middle of writing up and just didn't have the time, so I turned it down. But a few days ago I received my second request to review a paper. Since it's something I'll have to learn to do at some point, not to mention something that will become increasingly more important/common as I progress in my research career, I said yes.

This is basically how I feel about being a peer reviewer!

I'll be honest, I have very little idea what I'm supposed to do, or how I'm supposed to go about it. All I've got to go on are the referee's reports and feedback that I've received for my own papers. I had a look around for advice online, and there doesn't seem to be very much of it out there - the exception being the excellent 'AstroBetter' website, where I found a page with links to various pieces of advice for first time reviewers.

I don't really feel as though I'm ready for this -  I still think that my critical appraisal skills need a little bit of work, at least where other people's work is concerned - but I'm going to do my best.