Sainthood is not determined by the pope; sainthood is only officially recognized by the pope through the canonization process of the Catholic Church. In other words, all people who die in God’s friendship become saints. Canonization is an infallible statement by the Church that the saint is in heaven. - source
So the only difference between a “regular” saint and a canonized one is that we know for a fact that the latter are in heaven (canonization currently requires 2 miracles as proof.) While we can privately invoke the intercession of anyone we hope is in heaven or purgatory, a person cannot be invoked in public prayer—prayer done under Church auspices—until the Holy See has declared the person blessed.
Keep in mind that any ability or power attributed to any saint comes from God. No one has any power of their own except Him. So know that when we pray to the saints or the Blessed Virgin Mary, we know that it all ultimately flows from God alone.
*The intercession of fellow Christians—which is what the saints in heaven are—also clearly does not interfere with Christ’s unique mediatorship because in the four verses immediately preceding 1 Timothy 2:5, Paul says that Christians should interceed: “First of all, then, I urge that supplications, prayers, intercessions, and thanksgivings be made for all men, for kings and all who are in high positions, that we may lead a quiet and peaceable life, godly and respectful in every way. This is good, and pleasing to God our Savior, who desires all men to be saved and to come to the knowledge of the truth” (1 Tim. 2:1–4). Clearly, then, intercessory prayers offered by Christians on behalf of others is something “good and pleasing to God,” not something infringing on Christ’s role as mediator. * - article
Knowing that God is infinite, He could very well give them the ability to listen to every single prayer directed at them. Why not (and why limit God)? ANY saint can be asked to pray for us just like you can ask anyone you know to do the same. Patron saints are generally given such titles because of what they did in their lives or how the subject relates to them. A patron saint tends to be thought of the one “best suited” for their specific subject and generally you can hear a lot of people who pray to that saint and generally get results as proof of him/her being efficacious. Examples include St. Anthony as the patron of lost things.
*Not only do those in heaven pray with us, they also pray for us. In the book of Revelation, John sees that “the twenty-four elders [the leaders of the people of God in heaven] fell down before the Lamb, each holding a harp, and with golden bowls full of incense, which are the prayers of the saints” (Rev. 5:8). Thus the saints in heaven offer to God the prayers of the saints on earth.
Angels do the same thing: “[An] angel came and stood at the altar [in heaven] with a golden censer; and he was given much incense to mingle with the prayers of all the saints upon the golden altar before the throne; and the smoke of the incense rose with the prayers of the saints from the hand of the angel before God” (Rev. 8:3–4).* - source
As for how our prayers to them “work” exactly, nobody really knows. Maybe they just offer these prayers, or maybe He also gives them power to go and do these things that are being prayed for. Again though, keep in mind that it’s all ultimately through Him.