How can an author get assurance that his work will not be stolen by journal staff or reviewers?

It is unlikely that a reviewer or other participant in the peer review process will outright steal the work he/she is reviewing and publish it as original work, because it is easy to get caught.

If the "real" author of the work accuses the thief of plagiarism, the editor of the journal can verify that the work was originally submitted by the "real" author before it was published by the rogue reviewer. (Also see: What to do if a referee plagiarises the result after rejecting a paper?)

If the rogue reviewer is caught, the paper will be retracted (which is damaging to his professional reputation) and there may also be other consequences for the reviewer. See e.g. this recent example.

Let me add to @ff524's excellent answer. If you are paranoid, one way to add an additional safeguard would be to post a preprint on arxiv.org or a similar site. Then you have a public version with a verifiable timestamp, so even if all the journal's staff colluded to steal your idea, you could prove to the community that it was originally yours.

Here is the advise I got in a creative writing course a while ago:
Print out your article, book draft or whatever. Put it in an envelope and send it to yourself by registered mail (yes good old paper mail). Of course you keep all receipts and administrative documents you get at the post office. Don't open the letter when you receive it.
That gives you a formal and legally binding proof that your text existed at the time you posted it. In case of a formal dispute you have it opened in the presence of notary or whatever legal person can formally confirm the content of the document and the date.