(1.) The posts that are selected for review are the ones that (in the view of the StackExchange developers) are relatively more likely to be of low quality, which includes anything from being poorly formatted to outright spam. What you do when reviewing is, take a look at the post and see if it looks like a useful post and is on-topic. Then do whatever you would do if you encountered the post during your normal browsing of the site, for example:
(2.) If it's a good question/answer, upvote it. If it's spam, trolling, or other inappropriate material, flag it for removal. If it's a duplicate/off-topic/etc. question, vote to close. If it's a new question or a comment posted as an answer, flag it as not an answer. If the content is good but the formatting needs improvement, edit it. If you think of something else to say, whether good or bad, leave a comment. I don't think it's that complicated.
:) Of course, if the subject is outside your range of knowledge and you can't tell whether the post is good or bad, there's always the skip button.
The list of comment templates may come in handy. For more suggestions, refer to the Meta.StackOverflow thread "Can we agree on a review 'policy'?" (you should apply your discretion as there may be some differences between the communities, though most of the suggestions there seemed good to me when I just checked).
(3.) First posts are of course the first posts by new users. Late answers are answers recently posted by new users to old questions that have not had any activity for a long time. In either case, these are posted by new users who may not be familiar with how the StackExchange system works: they could be related questions posted as answers, comments that do not answer the question, or spam posts. Give them the same scrutiny you would give to posts otherwise, and consider leaving a comment to welcome the user and nudge them in the right direction if needed.