Hieroglyphs are the formal, written language of ancient Egypt.
Amazingly the written Egyptian language of hieroglyphic script seems to have popped up nearly fully formed 5,000 years ago. Slowly the language evolved over 3,000 years and developed several off-shoots. In addition to the standard, formal hieroglyphs, there was hieratic, a priestly cursive form, demotic, a cursive version used in daily life, and finally coptic, which was a version of the egyption language written in the greek alphabet.
Cartouches were always written using the formal hieroglyph characters which are described below.
The ancient egyptians used an alphabet with the characters representing sounds, just like "A", "B", "C" do do today for us. We call these graphical characters "glyphs". Ocassionally, a glyph will represent an actual thing, rather than a sound, but in these cases the glyph is a special "determinative" glyph (see below) or is marked off to let you know. The most common glyphs seen in inscriptions represent a single sound and these single sound glyphs are ofter refered to as the hieroglyphic alphabet:
Some of these sounds do not have true representation in American English phonetics. For example, the vulture (first glyph) has a sound somewhat similar to "ahh" but is really a stop like the middle of "uh-oh". However, remember that you don't need to pronounce the words and names you read. A few sounds can be represented by more than one glyph, for example the "y" sound can be drawn by a pair of reeds or a pair of slashes. It is thought to choice was made by what looked best in the inscription.
Next are some glyphs that represent two sounds. For example the duck in the top row, right side is very frequently paired with a sun disk and is found adjacent to king's names in cartouches. It is the sound "S-ah" and with the sun disk glyph "R-a" is the phrase "Sa Ra" meaning Son of Ra, the sun god.
There is a multitude of glyphs that represent three sounds.
Finally, for this introduction, there are glyphs called determinatives which tell the reader about the preceeding glyphs or actually represent a physical thing. Look for example at the kneeling man with his hands bound behind his back at the end of the second row. This glyph represents a prisoner.
Finally, hieroglyphics are read from left to right, or right to left and top to bottom. The direction is determined by the direction that animal or people glyphs are facing: read into the faces. Inscriptions are usually symmetric, if there is a hieroglyphic phrase on left side of a panel it will read left to right. The corresponding inscription on the other side of the panel will read right to left. If the glyph of a person or animal faces into a partural direction, the inscription will be read "into" that face. There are also some special cases. For example, a divinity like the sun god Ra (or Re) is a frequent component of a Pharaoh's name. The glyph for the divinity, sayRa (a sun disk), always preceeds the rest of the glyphs in the name because divinity has priority!