Saints are people whose testimony of faith extends beyond their lifetime. They are those whose exemplary lives continue to inspire. In Catholic thought, they are also understood to be companions to the living on their journey of faith. Through prayer to the saints, their intercession is requested in much the same way that living Christians might ask one another for intercessory prayer.
There is, so far as I know, no process for recognizing someone as a saint in the Independent Sacramental Movement (ISM). Generally the ISM churches simply recognize any saints from the Western or Eastern traditions.
As I've said, these are to be companions on our journey of faith, people to whom we pray, who then in turn pray for us. This is not the same thing as what Jesus does as our one mediator between the Father and humanity. While God the Son relates directly to God the Father, saints intercede for us through Jesus. At least, that's how I understand it. Mind you, I'm no expert on Catholic theology.
Here's where my Humanist skepticism kicks in. There are questions, such as: how do our prayers reach the saints? They are not omniscient, so how could they be aware of our prayers? The Church answers that God ensures that our petitions reach them, however that occurs. Then I wonder: how do they keep track of all the petitions? Some saints, like Saint Jude, are quite popular. They would have to be hearing hundreds of requests at a time, at least. They are not omnipotent. Finally, how would they even understand our prayers? Languages have changed over the centuries, and I suppose we can fall back on the notion that God translates for them. But then, how do they understand the content of our prayers, given how much the world has changed with technology and scientific progress?
So there you have the faith, and the doubts, around the saints.