When I pray to the saints, does the Church have a specific teaching on how I should do it? Word choice, syntax, ect? Do I pray to Patron saints for specific things related to their patronage?
Short answer, and possibly the only "approved" answer, is to check out the Proper of Saints in the Liturgy of the Hours (see universalis app). The prayers are usually short and may only suggest one or two virtues that the saint exemplified.
Other suggestion, St. Joseph is the Universal Patron, (i.e. for any need). See Fr. Calloway's consecration to St. Joseph for more info
Does the Catholic Church teach a specific way to pray to the saints?
Catholic piety and Church teaching go hand in hand here.
There is no particular manner or special way to talk with our friends in heaven. The Church leaves it to our personal preferences in regards to our piety devotions with the saints.
Just by coincidence, my wife mentioned to me that we never please in our prayers to the saints! That is an eye opener to myself!
We had a parish priest a couple of years ago and he wanted to do a novena to St. Joseph and St. Patrick, independent novenas! Great idea, however, he started his sermon by announcing he was going to have a parish novena to Saints Patty and Joe. I brought to his attention that if we want to pray to the saints we will have to start with having a profound respect for them.
Now back to the question at hand. Peter Turner’s answer is probably the best in my humble opinion. Using the collects of the mass as a means of prayer to the saints is excellent. If fact, it is quite traditional in some circles of Catholic devotion.
On another note saying novenas towards the saints is very powerful. There are literally hundreds of novenas. One of my favourites is the Novena of Grace in Honour of Saint Francis Xavier The Novena of Grace is quite famous.
Yet another form of devotional prayer to the saints comes in the form of litanies!
One of my personal favourite ways to pray to the saints is to read about a particular blessed or saint a make it something person. For example last year, I did a novena to Saint Corona to help us during the pandemic here in BC. I called it the St. Corona Challenge Novena. My wife and I, agreed to pray a novena to St. Corona which ended on May 14, her feast day. The challenge part was that we stayed home and isolated completely except for work, and doctor visits. We made sure not to buy groceries, go to restaurants or even out for coffee! On May 15 our churches were partially opened! Thank you, St. Corona.
As a Catholic I can say No.
While there are different prayers and novenas to petition various saints we can pray/ask them to help us any way we want.
They are ordinary people who through faith and the grace of God lived extraordinary lives but they should not be put on a pedestal (unless as a statue in a church lol)
A lot of saints have prayers to them based on their patronage. You could checkout this list of saints and find the prayers at the endo of the bios. They can serve as inspiration or a sort of template https://www.catholic.org/saints/