To get a peer review, submit an article to a journal.

The article needs to be in the proper format for the journal, and of a topic that is consistant with what the journal publishes. If the editor finds it believable or even plausible, it will be sent to other readers who have some expertise in the field.

For instance, the paleontologist that I do volunteer work for gets articles submitted to one of the journals on Cretaceous era dinosaurs. Ron (the paleontologist) has published many articles (including some encyclopedia entries) and has given many talks on these dinosaurs, so when a paper comes in that deals with his subject, he's often asked to review them.

In the case of a paper on material from or about Egypt, your paper would be sent to scholars familiar with that time period (people who can and do read hierglyphics and who are familiar with ALL the digs that have taken place on the Giza plateau and in its surrounding area.) It would also be sent to scholars who have visited the site and possibly geologists familiar with the formations there. If cultures other than Egypt are mentioned, your paper would be sent to one of those scholars.

Usually.

There are flaws in the system, and it can be hard to get unusual material in print (in the 1980's, JAMA rejected a paper I coauthored on physician mortality statistics... but Texas Journal of Epidemiology took it.)

The first step for getting a paper ready for publication is to have folks with degrees in the field you're addressing review it. So (for instance) when I do any paper analyzing data, I ask a mathemetician to glance over it and make sure I didn't make any ridiculous statements that would get the paper rejected.