Hi Lou,
The initiative system is based on a time count. Each combat turn is ten seconds long, and initiative determination is about identifying which of those seconds your attack will take place. Here's how it works:
Melee weapon: Roll a d10, that's the second you go on. In other words, high rolls are bad because they go later.
Readied missile weapon: Fires on second 1, then again at intervals determined by the weapon's firing time. For example, a readied Long Bow (firing time = 3) would go off on 1, 4, 7, and 10.
Non-readied missile weapon: Same as above, but the first shot goes at the end of the weapon's firing time. For example, a non-readied Long Bow would go off on 3, 6, and 9.
Spell: You can begin casting a spell on the first second of the turn, and normal casting time is equal to the spell's level. Thus, the spell goes off on the second equal to the spell's level plus 1 (e.g., a 4th level spell goes off on 5). If the caster is able to cast more than one spell per turn (see the table on p. 15), they can begin a new spell immediately when the previous one ends. For example, if a high level wizard cast a 4th level spell, then a 3rd level spell, then a 2nd level spell, they would go off on 5, 8, and 10.
I hope that helps.