[lvxferre]

A few things that I'd like to highlight, regarding decipherment of older languages.

You can somewhat guess which kind of script you're dealing with, by counting how many different graphemes there are. Something around 20-40 and likely got an alphabet, abjad, or similar; 100-200 and you're likely handling a syllabary; for a thousand and above, then there are at least some logograms mixed in, or the script is fully logographic. Mixed systems also pop up from time to time.

Egyptian hieroglyphs are in large logographic, and those are specially messy to recover. What Champollion did towards the phonetic part was no simple feat.

Another caveat is that sometimes a script offers more than one grapheme for each sound or syllable, or multiple sounds are associated with a single grapheme. Latin is a great example of that, with ⟨V⟩ representing /u: ʊ w ɨ/ (as in OO "boot", U in "put", W in "was", and a closed version of the A in "about"), while that /ɨ/ wasn't associated with any specific letter, sometimes being represented with ⟨V⟩ or sometimes ⟨I⟩. So you can't simply rule out a sound/sequence for a certain grapheme, just because it's already represented by another grapheme.

Living relatives of a language can give you valuable clues. For Egyptian this would be Coptic, one of its descendants; you can somewhat see things from other Afro-Asiatic languages in its grammar, but they're simply too distant to give you any sort of

You also need to take into account that languages change over time, and often diverge quite a bit from place to place. For example, that might mean that your /ka/ (kah) from one text is actually /ʃe/ (sheh) in another, so you need to be fairly certain on the time period and location of your sources.

Context is king, queen, bishop, knight, tower, and pawns. It's everything; and without that context, you will not be able to do anything. For Egyptian that context was provided by the Greek part of the Rosetta Stone, because it offered pretty much the same text translated into three versions (Greek, Demotic, Hieroglyphic), so the Greek part provided context and translation for the rest.