Most of the time, saints are regarded as patrons not because of any formal declaration by the church, but because of popular devotion. People in places, or professions, or situations of life may identify with this or that saint for various reasons, and the saint is then regarded as a “patron” for that group.
In quite a few cases, the means or instrument of a martyr’s death will cause a group that uses that instrument in their profession to regard the martyr as a patron. For example, Stephen was stoned to death, and so is the patron of stonemasons. St. Blaise was tortured with woolcombs, and so is the patron of woolcombers. St Apollonia had her teeth torn out with pliers, and so she is the patron of dentists. St Sebastian was shot with arrows, and so is the patron of archers, and St. Florian was drowned in a river, and so is the patron of firefighters – who use water (the means of Florian’s death) to put out fires.
You also have patrons derived from some of the legends associated with saints. For example, it was said that when St Ambrose preached, his words were so sweet to hear that bees used to swarm near his mouth, mistaking his sermons for honey. As a result, Ambrose is the patron of beekeepers. Because Joseph of Cupertino is said to have levitated while praying, he is the patron of aviators and airline pilots. Because St Antony Abbot was afflicted by the devil in the form of wild beasts, he (and not Francis of Assisi!) is the traditional patron saint of animals – and most especially of pigs.
People also look at the occupations of saints, and if they are in the same occupation they may regard the saint as a patron. Thus, St. Peter is the patron of fishermen, St Luke and Ss Cosmas and Damian are patrons of physicians, St George is one of the patrons of soldiers, St Isidore the Laborer is the patron of farmers, and St John Vianney is the patron of parish priests.