Generally speaking, your child can be around other kids once a fever has been gone for 24 hours and they are feeling better. If your child has been placed on an antibiotic for any reason, he or she should receive the medication for at least 24 hours before being around other students.
If you kept your children home every time they had the sniffles, they might never be in school. And the older they get, the harder it is to make up missed schoolwork. So if your child feels okay and doesn't have a fever, he or she should be in school. But, if your child has a fever (temperature over 100.0), body aches, extreme sleepiness, is vomiting, having bad diarrhea, coughing up a storm, has pain interfering with activity or really isn't feeling well, keep him at home until these symptoms are under control. Often it's the milder symptoms (such as slight runny nose and cough) that leave parents wondering what to do. Only you can make that decision, but be considerate of others. Before you take him out, think to yourself, would I want another child with the same symptoms around my son? If your child is not really sick, but something seems off, let the school nurse know and ask her to monitor your child.
You know your child best, so if you think something is wrong, don't send him to school. If you're concerned, call your pediatrician.