Heraldry is the knowledge and art of describing coats of arms. Pictures have nothing to do with heraldry - it's the descriptions that are important. To ensure that the pictures people draw after reading the descriptions are accurate, and reasonably alike, heraldic descriptions follow a set of rules.
A description of a coat of arms is called "blazon". To draw it is to emblazon it. The first thing the blazon describes is the tincture (colour) of the field (background), and then it describes the placement and tinctures of the different charges (objects) on the shield. The charges on a shield are decribed from the top to the base, from dexter to sinister. Dexter ('right' in Latin) is the left side of the shield, and sinister ('left') is the right. The reason for this is that they refer to the shield-bearer's point of view, not the observers.
There are seven tinctures, two metals and five colours.
Colour: Heraldic name: Gold Or Silver Argent Black Sable Red Gules Blue Azur Green Vert Purple Purpure
Later heraldry has introduced some more colours - brown (murray), sanguine (blood-red), light blue (ciel) and orange (tenné), but these are very uncommon. There are also a number of furs, like ermine or vair.
The first rule of heraldry is that you can never put metal upon metal, or colour upon colour. The main duty of an heraldic device is to be recognized. Colours are dark, metals are light.
The field can be divided into more than one colour. Common partitions of the field are 'parted per fess' (parted horizontally), 'parted per pale' (parted vertically), 'parted quarterly' or 'parted per cross' (parted horizontally and vertically), 'parted per bend' (diagonally from upper left to lower right), 'parted per bend sinister' (diagonally from upper right to lower left) and 'parted per saltire' (diagonally both ways).There are diminutives of charges as well. 'Barry of <number>' means that the background is divided into that number of horizontal stripes. There are diminutives of most partitions, like 'bendy of' or 'paly of'.
A shield vertically divided into blue (left side) and gold (right side) would be blazoned: Per pale azur and Or.
The partition lines are straight by default, but there are other kinds of lines as well. A line that looks like a saw's edge is "indented", and a line that looks like a sinus curve is "wavy".
A shield horizontally and vertically divided into red (upper left and lower right) and silver with sawedged lines would be blazoned: Quarterly indented gules and argent.
A partition variation is the counterchange. This is the term used to blazon a shield wherein the colors have been inversed across a partition line.
A shield which is green on the upper half and silver on the lower, charged at the center with a lion whose upper half is silver and lower half green, would be blazoned: Vert, a lion argent counterchanged per fess.
Charges can be animals, objects or geometric constructs (ordinaries).
Common animals are lions, leopards, martlets, eagles, gryphons, fish, boars or dolphins. There are dragons and unicorns as well, but they are not nearly as common as most people suppose. The default position of an animal is looking to the left. Animals are found in various different positions - a flying martlet is a 'martlet volant', a swimming dolphin is a 'dolphin naiant', and a walking lion is a 'lion passant'. Other words for positions are rampant (on hind legs), salient (leaping), sejant (sitting) and regardant (looking at the viewer). There are humans as well, although they are unusual, like wild men or saracens. If you show only the head of an animal, cut off at the neck, it is 'an <animal>'s head couped'.
Common objects are escallops (shells), crosses, mullets (stars), crescents, bugle-horns, water-bougets, gauntlets and different kinds of trees and plants. Circles are generally called roundels, but instead of being described 'a roundel vert', they have different named depending on colour. Bezants if they are golden, plates if silver, torteaus if red, hurts if blue, pellets if black and pommes if green. A roundel that is 'barry wavy argent and azure' is called a fountain.
Ordinaries are almost like partitions, but are handled like objects. A pale is a vertical charge starting from the top of the shield, ending at the bottom, and wide as a third of the shield's width. A fess is the same thing, only horizontal. There are also bends, saltires and crosses, as well as chiefs, bordures and chevrons. A chief is a fess situated in the upper third of the shield. A chevron looks like a saw's tooth, arching from the middle of the left side of the shield to the middle of the right.
If you put a mullet on a bend, the bend 'is charged with' the mullet.
Full descriptions of coats of arms could look as follows:
Argent, on a fess azure between in chief two anchors crossed in saltire sable and in base a lion passant gules a fleur-de-lis Or.
Sable, two swords crossed in saltire argent, between four fleurs-de-lis Or, all contained within a bordure purpure.
Party per fess argent and sable, in chief a falcon close vert, in base a plate charged with a fleur-de-lis vert.
There are, of course, more complicated designs:
Party per fess: The chief Argent, charged with five bezants, the centre bezant charged in chief with a latin cross of the field, on a canton in sinister base of the first, a bucket: The base party per pale Azure and Argent, the dexter side charged with three rings conjoined at their centres in pairle, the sinister side charged with a bend sinister Azure bearing three quatrefoil of the field. Behind the shield a pastoral staff. The shield contained within a cartouche and ensigned with an ecclesiastical hat supporting six tassels on either side of the shield.