Initiative is rolled on a d6. One player for the party is designated by the DM to roll initiative for the whole player party. The DM then rolls an initiative die for all combatants opposed to the party. The two dice are then compared. The party of combatants with the highest roll has won initiative.
This is made complicated, however, because some creatures with sufficient dexterity receive a modifier to the die rolled (+1 for a 16 dexterity, +2 for a 17 dexterity and +3 for an 18 or better dexterity) or receives an adjustment from some other source (luck or a magic item). In all cases, the die rolled for each side is adjusted individually for members of the party.
For example, Albert, Bala, Caleb and Drusilla comprise a party of player character combatants facing a group of orcs. The DM designates Bala as the player who will roll a d6 for the party's initiative. She rolls a 3. The orcs roll a 5. Normally, this would mean that the orcs had initiative. However, it so happens that Drusilla has an 18 dexterity, allowing her a +3 modifier to initiative rolls. This gives her a personal initiative roll of 6 (3+3). Caleb has a 16 dexterity, so he has a bonus as well - but as his bonus is only +1, this is not enough to challenge the orc's roll. Caleb's personal initiative is only 4 (3+1). Albert and Bala do not have sufficient dexterities to gain any bonus.
Thus, Drusilla has a 6 initiative, so she goes first. The orcs have an initiative of 5, so they go after Drusilla. Then the rest of the player characters, including Caleb, end the round.
Take note, however, that since the rest of the player party would then be followed by Drusilla, all the players in the party are free to act together. It is only necessary to roll initiative once. Afterwards, the turn-based combat system simply flips back and forth between the player characters and the enemy. The pattern, however, is disrupted by stunning rules - but for those familiar with traditional 1e rules (AD&D), the policy of rolling initiative over and over is dispensed with.
Once initiative has been determined, the combatants possessed of it may take whatever action they feel is appropriate, in the bounds of the rules and role-playing.
Simultaneous AttacksIf it should happen that opposing combatants end with the same value on their adjusted initiative die, then combat for those combatants will be considered simultaneous. Where simultaneous attacks are indicated, all combatants are considered to move and attack regardless of the actions of the enemy. This means that if the enemy is hit by a combatant and stunned, the enemy will still be entitled to attack, as both attacks are considered to happen at the same time.
If necessary, the action points (AP) expended by either side may need to be played out 1 AP at a time (but only in relation to movement or preparation of materials, drawing weapons and so on). If this is the case, then actions can be scaled according to this table:
Above is a very standard wargame process - the left hand column indicates the total number of AP possessed by the combatant. As the row at the top is counted from 1 to 8, participants act according to their total AP. Thus a combatant with 4 AP would be free to expend 1 AP with the 2nd column where as a combatant with 3 AP would not be able to expend an AP until the 3rd column. Thus, it should be presumed that the combatant able to act first would be the one that took control of a given hex or grabbed a weapon first.
Note, a combatant with 5 AP would have time to draw a dagger and still have time to tie for possession of that hex with a combatant possessing 2 AP - in such a case, the combatant with the next move would succeed against the other. This means the character with 5 AP would ultimately move, despite having performed a different action.
Regardless of the number of moves available to both combatants (assuming the minimum necessary to attack), all combatants are entitled to attack during a simultaneous initiative, regardless of the table shown.
Combatants are considered to remain simultaneous until one or the other is stunned - if both are stunned, then they remain simultaneous until being stunned again. As troublesome as this may seem, it is rarely an issue. Usually, it applies to only individuals and matter is settled either by one being stunned or both combatants are far enough apart on the battlefield that the simultaneous effect can be ignored.
See Attacking in Combat