It depends on the language, in part it's guessing. But educated guessing!

There is no one Ancient Egyptian, the term usually conjures up ideas of the varieties that were written using heiroglyphs, which span a period of time of over two millennia. For comparison, that's less more than the amount of time between Classical Latin and the modern Romance languages!

We don't really know the exact pronunciation of Ancient Egyptian, but we can determine the basics of the phonological system. It'd be for example, like knowing that the English words two and do rhyme and that only the first sound is different. As well as a vague idea of what kind of sound it is.

There are a few sources, you can take a look at the modern descendant, Coptic, which is still used as a liturgical language. There are also loanwords in other languages that can give you an idea. Combining this information to make projections backwards is called Comparative Lingustics and it even allows you to recreate unattested languages, that is, languages that were never written down and for which we have no direct evidence. This is how languages like Proto Indo-european were worked out.

More specifically for Egyptian, Heiroglyphs also make use of similar sounding words at times so you can determine some similarities, this would be, for example, like an English speaker using an image of an eye to represent the word I because they sound alike.

Using all of these methods, you can reach an approximation, but it's likely the real thing sounded completely different and of course, it also varied a lot depending on the timeframe. So this means that that scene in the Mummy where Rachel Weisz reads from the Book of the Dead definitely does not represent how the Ancient Egyptians would've said it.

With more recent ancient languages, like Latin, it's pretty much all worked out because there are actual style guides that not only indicate the "correct" pronunciation but what kind of pronunciation was commonly used. Oculo non oclo, cf. French œil, Spanish ojo, and Portuguese olho.

Not to mention, the vast amount of Romance languages allows for more comparisons to be made. So you could definitely read the work of Cato and Cicero in a pronunciation that might be lacking some details but to the writers themselves would be perfectly understandable and recognizable as their own tongue.

So this all varies a lot depending on the evidence you have. Comparative Linguistics gets you so far, but the more extant languages you have, the better, and then other resources can be really helpful. If a future linguist were to find /r/boneappletea for example, they would be very happy.

edit: I can't word good

You might want to check out this recent answer by /u/UndercoverClassicist about Egyptian hieroglyphics, Linear B (which can be pronounced and understood), and Linear A (which we can pronounce, but can't understand): Has there been any real progress in deciphering Linear A Language?