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Attacking with a goaded creature doesn't cause it to stop being goaded. If there is an additional combat phase that turn, or if another player gains control of it before it stops being goaded, it must attack again if able.

If a creature you control has been goaded by multiple opponents, it must attack one of your opponents that hasn't goaded it, as that fulfills the maximum number of goad requirements. If a creature you control has been goaded by each of your opponents, the creature must attack an opponent (rather than a planeswalker or battle), but you choose which opponent it attacks.

If the creature doesn't meet any of the above exceptions and can attack, it must attack a player other than the controller of the spell or ability that goaded it if able. If the creature can't attack any of those players but could otherwise attack, it must attack a planeswalker an opponent controls, a battle an opponent controls, or a player who goaded it.

If, during a player's declare attackers step, a creature that player controls that's been goaded is tapped, is affected by a spell or ability that says it can't attack, or hasn't been under that player's control continuously since the turn began (and doesn't have haste), then it doesn't attack. If there's a cost associated with having a creature attack a player, its controller isn't forced to pay that cost, so it doesn't have to attack that player.

Being goaded isn't an ability the creature has. Once it's been goaded, it must attack as detailed above even if it loses all abilities.

If a creature can't have +1/+1 counters put on it, its controller can't choose it just to have it become goaded. If it can have counters put on it but replacement effects cause it not to receive +1/+1 counters, it doesn't become goaded.

As Agitator Ant's ability resolves, first you choose which creature you control, if any, to put two +1/+1 counters on, then each other player in turn order does the same, knowing the choices made before them. Then each chosen creature receives its +1/+1 counters and becomes goaded.