Tell your boss that you'd like to review. They're usually more than happy to delegate the task.

Well most often the journals will just find you since they look for experts in the field based on previous publications. But if you really want to do more reviewing I would choose a few journals that interest you most. Oftentimes you can sign up as a potential reviewer at the journal website. Sometimes you can register for a whole publisher and indicate your expertise. Alternatively you can just write the editors. It might be a good idea to have an online list of publications that you can point them to. In fact that list itself might be found by editors looking for a reviewer.

Have you been in contact with organisers of conferences relevant to your skill base? They are usually keen to have extra hands for sifting through papers. Their contact details will be found on the conference proceedings. As for journals, I am surprised that you have not been asked already as they usually use authors from published papers as referees.

I have never referred any paper or conference, but I have some suggestions:

• start a blog, and use it to write about papers on the field you are working on. Whenever you write a blog post about an article, send an email to the corresponding authors, inviting him to read your post and make comments. This way you will make more contacts and increase the probability of being asked to be a referee. If you don't have the time to have a blog, use at least twitter.
• start contributing to open-source projects, and subscribe to mailing lists such as biopython-dev or bioperl-dev. Sometimes, the organizers of opensource-related conferences write in those mailing lists to ask whether anybody is interested in helping organizing it.
• organize a conference yourself :-)

1. Become a corresponding author, ie leave your email in the paper.

2. If your boss or your friends have reviewed before, ask them to recommend you when they want to reject a review invitation.

3. Some people contact associate editors to ask for review experiences. I do not know if this really works. Editors should have a better answer.

EDIT: IMHO (I do not have any editorial experiences), there are three ways for an editor to find reviewers. Firstly, when we submit a manuscript, many journals require to provide a list of recommended referees. The editors will usually try a few in the list if they think the list is reasonable. If you want to be recruited this way, you have to let people know your email address some way, e.g. as a corresponding author or making your software/algorithms well known to the community. Secondly, editors may ask people they are familiar with. These people may be their friends/colleagues or have reviewed manuscripts before and given good reviews. This way is for returned reviewers. Thirdly, when the potential reviewers of the first two types reject the review invitation, they are frequently asked to provide other reviewer candidates and frequently they give colleagues/students they know. This is why seeking help from your boss and experienced friends can be very useful. I guess the first paper I reviewed came to me in this 3rd way, but I cannot confirm this.

Why would anybody want to review papers for journals and conferences? Most people (me included) try to reduces these chores to a manageable level (by either being 'permanently unavaible', by inventing conflicts of interest, or by several other means that I won't disclose :-) (just in case there are editors reading BioStar)

But seriously, you either must live in a very different 'European country' than the ones I know of, or your research area works different from mine (what is TCS, by the way?). I have never heard of cases where paper reviewing is considered an asset for a C.V., mostly because this is done blindly and thus nobody can check how many papers you have really reviewed.

If, on the other hand, your desire is to help the scientific community, doing peer review for journals or meetings is a laudable thing. As others have pointed out, you normally don't have to do anything, the journals will find you. The usual prerequisite is that you have to be a PI (i.e. group leader) and that you have published in the field of interest (as a corresponding author).

Journals normally don't as postdocs or other non-PIs for doing reviews. However, I suspect that a large portion of paper reviews is done by postdocs, because the PI has deferred the job. The journals don't like this practise but there is not much they can do about it. Often they don't even notice because the review goes by the name of the PI.