If one of your friends or alliance members is in trouble and needs help, you can send some of your Triremes with a shipment of troops and supplies. Up to 5 shipments can be sent at any given time, and one additional shipment can be sent every 1 hour.
In a single aid shipment, you can send up to 20% of your dominion's currently available Spearmen, War Elephants, Fire Ships, Triremes, Money, Knowledge, and Grain to another dominion.
No matter what you wish to send, you must send a minimum number of Triremes to deliver your shipment, where the amount is based on the size of your dominion. If you specify a number smaller than this amount, any remaining Triremes will be automatically recommanded to you once your shipment is delivered.
Aid can only be sent to those who actually need it - a dominion whose networth is significantly greater than yours likely has no need for your goods. However, if you are in a clan, you will be allowed to send goods to alliance members many times your size.
It is not possible to send aid to those you are at war with - the very idea is laughable.