If I believe my child has adhd, what symptoms should I look for?

Depends on age. Adhd typically is diagnosed around age 6-7 years of age, mostly because those without adhd are much less likely by then to have the symptoms of poor attention, high distractibility, high physical activity, & poor impulse control that we use to make the diagnosis. Persistent issues in several of these domains in various settings (not just home or school) warrant an assessment if causing problems.
ADHD. The main features of adhd are inattentiveness, impulsiveness and hyperactivity. Children with adhd have trouble focusing, organizing, or may seem to 'daydream' a lot. They are often in constant motion and talking out of turn. They tend to interrupt, blurt out answers and have trouble waiting for their turn. It is important to talk to your doctor, because adhd can be confused with other issues.