Both the common cold and seasonal flu are caused by viruses (it's a myth that colds are caused by being out in cold weather). The CDC reports over 200 viruses as the culprits of colds, with the rhinovirus being the most common. There are 3 types of flu strains -- A, B, and C -- though the AAP cites A and B as the ones most likely responsible for most flu bouts.
The viruses that cause colds and the flu are transferred by touching or coming in contact with infected surfaces, or infected droplets emitted from coughs or sneezes. You know the drill: an infected kid wipes his nose with his hand (and, being a kid, doesn't immediately wash or sanitize it), then touches one of the classroom toys; your kid comes along, picks up the toy, then scratches her nose before washing her hands…next thing you know, she's home sick.
Since the common cold and seasonal flu are so well known, you can probably diagnose your child based on the description of the symptoms. Be sure to contact your pediatrician at the first sign of symptoms if your child is younger than 3 months, or if she shows any signs of breathing difficulties, persistent fever, has a cough or runny nose that won't go away, ear pain, lips or nails turning blue, or excessive fatigue or crankiness.