Once again? It depends :D
In the early history of heraldry, the answer is 'whatever worked'. Remembering that in heraldry, the original aim is to be able to tell two people apart on the field of battle, the son would bear something that looked like his father's colours, but with some form of difference, also known as a mark of cadency. On the death of his father, if he was the eldest son and heir, he'd inherit his father's arms (or is parents, if their arms were marshalled).
As time went by, theses differences were formally codified, particularly in England and Scotland. In England, these marks of cadency (also known as brisures, from the French verb briser, "to break") are as follows:
- first son, a label of three points
- second son, a crescent (the points upward);
- third son, a mullet;
- fourth son, a martlet;
- fifth son, an annulet (a ring);
- sixth son, a fleur-de-lys;
- seventh son, a rose;
- eighth son, a cross moline;
- ninth son, a double quatrefoil.
In England, these are voluntary, as the principle of 'one man, one coat of arms' is honoured considerably more in the breach than the observance: they are only really used when there is some important reason to distinguish two branches of a family.
In Scotland, however? Oh boy. The label is used for the first son, but after that a complex system of variously coloured and styled borders is used. For more detail than you could possibly ever want, check the Wikipedia article on the subject and its references, as well a set of images of the current cadency marks for the British Royal Family (who, of course, just have to be different!)
Heraldry being, historically, a tool to distinguish fighting men on the battlefield, has for the most part not adopted cadency marks for daughters (cue 21st century outrage at this point). It's worth noting that Canadian heraldy (for one) however has.
It has to be said, in the earlier periods we game in (11th century on), we're dealing with the 'whatever works' period of heraldry, and applying formal rules that probably weren't invented then is a last-ditch replacement for doing the research, if you can. By the 15th century (War of the Roses etc), to be fair, things get a little more formalised.
Anyway. Next? Borders and backgrounds. Till then, have fun!