A Field can be of a single colour or fur, or it can be divided, or Parted, into multiple parts, and each one coloured (or furred) separately. Each of these lines of partition has it's own name. A vertical part is known as party per pale (or just per pale). Horizontal is per fess, diagonal from upper left to lower right is per bend, while the reverse is per bend sinister. If it's divided into fourths, alternating colours, it's called quarterly, unless it's divided diagonally, in which case it becomes per saltire. Per chevron is sort of an odd one, looking somewhat like a single-peaked mountain. Less common (and not shown) are the "triple" divisions of per pall and per tierce. Per pall is essentially a combination of per chevron and per pale, creating three divisions: equal sides, and the "triangle" rising from base. Per tierce is simply three vertical divisions, and would probably be just as easily blazoned as "per pale" with a Pale of a third colour.

The lines of partition can also be multiplied to create patterns. For example, per pale multiplied becomes paly, per bend becomes bendy, and per chevron becomes chevronny. Quarterly multiplied, however, becomes checky (or chequey), and per saltire becomes lozengy. Paly and bendy mixed becomes paly bendy. When blazoning, it is not necessary to capitalize the lines of partition.
The straight lines of partition or ordinary may also be decorated in numerous ways. Engrailed, for example, is formed of continuous semicircles, joined at the points, and with the points pointing "outwards," away from the "most honourable position." (Remember in Heraldry, the dexter, or left, is more important than the sinister, or right side, and the chief, or upper area takes precedence over the base.) So, in the case of a shield blazoned as "Per fess engrailed" the points would point downwards. If it were "Per bend engrailed" the points would point towards the dexter base, as right-left orientation is considered more important than top-bottom in these cases. Invected is the opposite of engrailed, having the points going "inwards."
Wavy or Undy is inspired by water, and has a smooth up and down wavy appearance, as in a sine wave. Nebuly, which comes from clouds, is a more pronounced wave, with a sort of bubble at the peak and trough. It rather resembles the tips of jigsaw puzzles in some depictions, however, artistic variation can create a number of different looks.
Indented and Dancetty (or Dancetté) really have to be discussed together, because they are nearly identical. In fact, the only real difference is that while both are composed of a serious of upward and downward angled lines, reminiscent of mountains, Indented may be composed of any number of peaks, while Dancetty is depicted with a limited number of peaks spanning the width of the field - typically only three. Dancetty is also usually only found in fess and chief divisions, and the occasional bend. In the case of a Fess Dancetty, there will be three peaks on top, and three on bottom.
Embattled is a very common form of decoration for lines of partition and ordinaries. Also known as Crenellé, it is composed of a series of crenallations, as in the top of castle battlements. The only special considerations for this decoration are in the case of a Fess, Bar, Chevron or Bend, all of which are only Embattled on the top unless specified as Embattled and Counter-embattled, which indicates Embattling on both sides of these particular ordinaries. Normally, the embattlements and indentations are complementary in this case - with an embattlement opposite an indentation. The term Bretessé is used to indicate an opposed Counter-embattling, that is, indentations appear opposite indentations and embattlements opposite embattlements. A very rare form, known as Embattled Grady, resembles a series of stairsteps up and down, and is seldom seen outside of the Fess or Bar. Raguly appears very similar to Embattled, except that the crenallations are slanted. Although in a pale or bend the teeth should point upwards, there is no definite indication that on a fess or other horizontal line that the teeth should more accurately point to the dexter or sinister. If pressed I would say to dexter, as that is the more common rule to follow.
Dovetailed is a more modern convention, with the line of division resembling, as the name suggests, dovetailing. Potenty (or Potenté) resembles the fur Potent in form.
Recently, Arched and Double-arched have come into use, primarily as a decoration for the Chief, however, there is no reason why it could not also be used to decorate a Fess or Bend. In both cases, the form is of a simple arc or two spanning the field.
Urdy and Rayonny, although quite different in form, are similar in that neither are found typically in lines of partition, but usually only as decorations for ordinaries (usually only crosses at that). Urdy looks somewhat like picket fence tops, upwards and reversed, while Rayonny is quite obviously the depiction of the rays of the sun, or perhaps flames.
Flory counter-flory is a quite beautiful line of partition (not usually used for ordinaries), consisting of a succession of fluer-de-lis alternately reversed and counterchanged. If this line is used on an ordinary, only half of the fleur-de-lis is depicted, that half being the the half on the outside of the ordinary.