I've thought a bit about how to answer this question over the last few days. There are a couple things I'd like to note before discussing how reviewing "correctly" (this is hazy; more on this later) works.
The first is that review bans are very, very uncommon. I could probably count all of them on one or two hands. Most of the advice I'll give here should be pretty intuitive if you take the time to read the content you're reviewing. If you're well-intentioned and paying enough attention, you're not going to run into a review ban.
The second is that review bans are seriously unlikely to be held against you in the long-term if you're making a genuine effort to improve. Nobody has, to date, needed to be stopped twice.
As far as actual advice on reviewing, I'll start with what I consider the tenets of reviews:
- Reviews are driven by the community. You are the community. So, if you all decide to review a certain way, that's going to be what will happen. In the absence of other information, don't be afraid to go with what seems right; it probably is.
- If you're confused about a review, everyone else probably is, too, and going with the best choice might be a good idea.
- If you're extremely confused about a review, it might be a good idea to skip it.
- Most of the knowledge you need can be gained through participation in the site.
- You can always follow up on a review to see what happened with it, including the reviews you've skipped, by checking your review history.
- If you don't understand why a review was completed in a certain way, Meta is here for you, and nobody's going to hold a question about it against you. For that matter, if you're not sure why a question was closed, or notice a close-war on a question, feel free to ask here, too.
It's a good idea to be aware of site practices, and this is something you're likely to have already picked up through normal participation. Most of what follows here should be fairly intuitive, but I'll go into detail anyway.
First Posts: I'll start here because this is always the problem child of review.
The one thing that causes new users to leave most often is a lack of human interaction. Don't let new users ask or answer into the void. No Action Needed is almost always flat-out wrong. You are the only one to review a user's first post; bear this in mind when reviewing.
When reviewing FP, the ideal is to leave a helpful comment about their post. Barring that, upvote an existing helpful comment, and barring that, at the very least, please try to vote (or, if need be, flag). You might need to read the question as well as the answer, too.
If you can't think of a helpful comment to leave, nobody else has said anything, the post isn't worth either an up or downvote, and it doesn't need to be flagged, then consider either skipping or calling it no action needed.
Close queue: It would be nice to be aware of the justifications for the existing close reasons. However, they're supposed to be relatively understandable to a new user, so using them where it feels applicable is a good idea.
Also note that you're one of five reviews in the close queue, so if you make one error here or there, or unintentionally apply the wrong close reason, it's not going to have a tangible impact on the site function. This isn't to say being careless is a good idea, obviously.
Suggested edits: This one's pretty straightforward. Don't approve code block markup where it doesn't belong. Approve/improve edits that increase the clarity of the post, and catch most or all of the problems with it. Reject/improve and reject edits that miss most or all problems, or cause new problems, or edit in irrelevant content, or are vandalism/spam/etc.
Low quality posts: There's only one policy to be aware of, which is that answers need to have a reasonable amount of justification to them. If they lack justification, they should be deleted.
Note: answers shouldn't be deleted if they're wrong; wrong answers should be downvoted instead. An answer that is wrong but thorough and complete Looks OK.
Tag wiki edits: Most people aren't too sure about this, so don't feel awkward if you aren't either. Tag wikis are weird. The general guideline is: excerpts guide the user as to when to use the tag; wikis guide the user when they want to learn more about a topic. Try to adhere to these guidelines when suggesting and reviewing edits.
Well, this ended up being a lot more words than I thought it would. Sorry 'bout that. Hopefully it's complete, though.