“How can I improve my child's speech?”

I would start by speaking with the pediatrician if you have one. They may refer your child to have a hearing evaluation and a speech/language evaluation. 

Speech problems" is not specific. You need to ask the doctor for a prescription order for speech therapy evaluation or a referral for a speech pathology consult and you need to get an assessment from a speech language pathologist and work with that professional on your kids needs. Early intervention is key so don't stop asking until you get a doctor to write you a referral order for speech therapy evaluation.