Taking a standard at random from Wiki:
(this is a Scottish baronet's standard - Macdonald of Sleat)
The CoA, as you say, comes first (reading from the staff).
The field of the banner is either of the principal colours of the CoA, or the livery colour(s). It is often, as here, party per fess, but may be of a single tincture or, very rarely, barry of four (which begins to look messy when coupled with the next element.
The field is divided into three by two bendlets bearing the motto. (I have seen one standard where this element did not contain the motto (presumably the armiger did not have one) and an embroidered pattern was substituted.)
In each of the three compartments created by the "motto bendlets" is placed the badge, or (as in my forthcoming standard) badge/crest/badge, or some alternative arrangement (the example apparently has crest+torse/crest+torse/badge).
The standard these days has the end pictured above (which can hardly be called "swallow-tailed") if one is a knight or of higher rank, or rounded for esquires and gentlemen.
(As corrected following a later post.)The whole concoction is fringed in the colours of the field.
There are minor differences of practice between the College of Arms and Lord Lyon, and significant differences in entitlement (which need not concern a citizen of the US). No doubt other jurisdictions have their own variations, but this should get you started I hope.