For thousands of years, no one could read the hieroglyphic writing of Egypt. No cryptologist could decode it. Thousands of years of scholarship were privated by this bizarre form of writing. Then, when Napoleon's army marched through Alexandria, a soldier discovered a stone which contained three forms of writing: the ancient picture-writing, hieratic (a simplified "shorthand" hieroglyphic script, about as different as our cursive hand is from ancient Roman monumental letter), and Ancient Greek. The stone had the same message, written three times in two different languages (in Greek, and twice in Egyptian — once in hieroglyphics and once in hieratic). By comparing the names as they occured in the two languages, researchers could figure out which symbols were supposed to be which sounds.
It's a common misconception that hieroglyphics were ideographic, being pictures rather than letters. In actual fact, most hieroglyphic symbols were letters, representing from one to three sounds each. In the case of frequently-used words, an abbreviation might be used, and in the case of homonyms or unclear meanings, an ideographic determinative would be added — for example, a little picture of a person after someone's name to show it was a name.
As Gone Jackal says, the Ancient Egyptians didn't write vowels; their "alphabet" consisted purely of consonant sounds. Egyptians would sometimes write long vowels as a "y" (long "i" or maybe "e"), "w" (long "u" or maybe "o"), or aleph (long "a"). The rest of the time, the vowels are purely guesswork, and most scholars don't even bother to guess, writing only the consonental "skeleton" of a word.
The "aleph" (glottal stop) isn't phonemic in English, but it does occur sometimes, usually at the beginnings of sentences which contain vowels. The glottal stop can also occur in some dialects as an allophone of "t" — for example, the word bottle can be pronounced "bo'l." This happens in Cockney dialect. It's the sound that comes at the beginning of each part of "uh-oh". The symbol of the aleph looks kinda like an eagle or vulture.
The Egyptians used a picture of a feather to represent a "y" (palatal glide), like the first sound in the English word yes. This symbol also sometimes represented the combination of glottal stop + "i." When two feathers occured together, it represented a long "i" or "y."
The Egyptians also had a sound akin to that of Hebrew and Arabic's "ayin." This, as far as I can tell, just doesn't occur in English at all. It's the voiced equivalent of the pharyngeal fricative which I'll describe below. It's kinda like the sound Homer Simpson makes when thinking about doughnuts. The symbol used to represent this sound was an arm with an open hand. This is the second sound in the name of the Sun God, Ra — which was pronounced more like "Raugh." (Like, "Doughnuts, augh.")
To represent the palato-velar glide ("w"), the Egyptians used a picture of a little chick, or a little curl.
To represent "b," they used a picture of a leg and foot.
To represent "p," they used a little square.
A picture of a horned viper represented "f."
The bilabial nasal "m" was represented most often with a picture of an owl, though it could also occur as a forked staff or a length of rope folded once.
The "n" sound was represented as a series of waves on the Nile.
The Egyptians used an ovoid slit, representing parted lips on a human mouth, as the symbol for "r." This "r," unlike in most languages, is not trilled — it is an alveolar approximant, like an English or Mandarin "r." The Egyptians didn't have an "l" sound in their language, because the "r" was so close it would have caused problems, much like in Japanese and unlike English or Mandarin. The Egyptian word for "Lebanon," for example, was "Remenen." When transcribing foreign words which contained an "l" sound, the Egyptians used a picture of a lion, the biliteral symbol for "r" + "w."
Gone Jackal is accurate in saying that the Egyptians had four different kinds of "h." Sometimes, it is difficult for English speakers to figure out the differences between these sounds. In English — at least in my dialect — three of these four occur as allophones. In other words, I say all three as a matter of course every day, but I use them all for "h," not as separate letters. The Egyptians used them as separate letters.
For the "conventional" "h" as in hot or happy, the Egyptians drew a little floormap of a hut.
The "aspirated" dotted-"h" that Gone Jackal describes is the pharyngeal fricative. I say it when I say the word hold. It occurs deep in the back of the throat. The symbol for this was a twisted chord.
The letter which we normally transcribe as an "h" with a little curve underneath is pronounced like "ch" in loch or German Bach. It was represented as a shaded circle.
The "h" which represents the "ch" of German ich — I say this letter when I say the word heap — is transcribed as an "h" with a little bar underneath. The Egyptians wrote it as a string of animal gore — I think maybe the throat tract.
The letter "s" was written as a crooked staff, or a doorlock. At an earlier time, the doorlock represented a "z," but eventually the two sounds coincided.
The "sh" sound was represented as a writing tablet.
"Qof" (the Arabic name; the Greek and Hebrew name for the sound is "qoppa") is kinda like a "k" sound, but pronounced by touching the back of the throat against the soft palate. It can make you gag the first few times you try it, but it's actually a pretty common sound outside of Europe. It occurs in Hebrew, Arabic, Inuktitut, Klingon, Iranian (I think) and many more. And, of course, Ancient Egyptian, where it was represented by a little sloping hill.
The "normal" "k" sound was represented by a picture of a bowl.
A little tent or temple symbolised the "g" sound.
A stylised loaf of bread — basically just a semi-circle — represented the sound "t."
A length of rope, folded once and knotted at both ends, represented the sound "ch" as in English church, which linguists translate as a "t" with a small bar underneath.
A closed hand, turned upwards, represented the sound "d."
A curling snake (with no horns) represented the sound "j" as in judge, which linguists transcribe as a "d" with a small bar underneath.
Aside from these letters, the Egyptians also used some letters to represent two or even three consecutive sounds. For example, a picture of an eye represented the sounds "y" + "r." Also, different standard symbols were used in cases where space was a concern.
Lots of info is available on the Web regarding Egyptian pronunciation. My favourite is Jim Loy's page, found at http://www.mcn.net/~jimloy/egypt.html.