This is a common misconception of the Catholic church. I am a practicing Catholic, and here is what is the view of the Catholic church.
When you have a problem, illness, etc... and you pray to the virgin mary, a saint, etc...you are not praying to that saint or person to solve your problem for you or to worship that person. What you are doing is asking that saint, virgin mary, etc... to pray for you to God. An example I can give is the confession prayer:
I confess to you almighty God,
and to you,
my brothers and sisters,
that I have sinned through my own fault,
in my thoughts and in my words,
in what I have done and what I have failed to do,
and I ask the blessed Mary,
ever virgin,
all the angels and saints,
and you,
my brothers and sisters,
to pray for me to the lord our God.
This is not meant to circumvent your prayers to God, just to ask others to pray for you. Obviously I'm not here to debate the right or wrong of religion/Catholicism, I just wanted to make sure to bring some clarity as to the actual views of the church.