At what age do patients with downs syndrome begin trying to talk?

Complicated. Most children with down syndrome will have delayed speech and many of these children will have anatomical and functional ear problems that dispose them to varying degrees of deafness. They must be screened early as they may benefit from surgery and hearing aids. I have an unfortunate patient who has down syndrome and is autistic. He is 10 and has almost no speech. Yes, complicated.
Quite variable. Down syndrome kids have quite a diverse variability in communication skills. Some have use words as early as a year and some 6yr or later. Early studies showed 34mo as an average with and by 5yr in most. Use of sign language in these infants can bridge the gap for basic needs and does not interfere with later skills.
Varies. It varies but averges a bit later than other children. Your pediatrician should have special growth curves, and guidelines for development specifically for children with down syndrome in your child's chart. There are even special labs and stays your child needs at specific times.