The nose is probably one of the most underappreciated "organs" in the body. The human nose has several functions including to smell (to detect danger, food, poopy diapers, or pretty flowers), to heat and humidify air before it gets to the lungs (otherwise one would start "hocking nasty loogies"), and most importantly to filter air. To filter the air there are multiple mechanisms involved including turbinates, a mucus layer to trap germs/dust/allergens, a microscopic layer of hair to move the mucus, and a robust immune system that reacts to things (adenoids in the back of the nose as an example)
A stuffy nose is one of the most common symptoms a child will experience. Congestion (meaning you can't breath well through the nose) is usually due to inflammation (or swelling) of the inside of the nose. This is a standard reaction to infections, allergies, and irritants. Usually it resolves without treatment but if it is lasting more than a week or two then consider seeing your child's pediatrician. Starting out with saline spray to the nose is an easy starting point to clean it out. Motrin can also provide some relief (if over 6 mos of age and no restrictions from Motrin use). Chronic nasal congestion (longer than 4-6 weeks) can at times be managed with the use of a nasal steroid. For nasal congestion lasting longer than two months a talk with your friendly neighborhood pediatric otolaryngologist is a good idea. Depending on the situation, longer use of nasal steroids or a quick surgical intervention (adenoidectomy, turbinate reduction) can be used.
Runny Nose (Rhinorrhea)
A runny nose is also a very common symptom children will encounter. Mucus from the nose can be clear and just a little, to colorful (green/yellow) and copius. Clear drainage is most commonly due to the nose encountering irritants - including dust, allergens (pet dander, pollen, etc), and germs. Using saline spray to clean the nose out in these cases can sometimes prevent the those irritants from progressing to an infection or inflammation. If allergies are suspected then trying an antihistamine like zyrtec or claritin is usually safe (though if less than a year old consult your pediatrician first). If the drainage is colorful and lasting more than a couple of weeks then it could be a sinus infection and your child should see their pediatrician (also see next section).
The common cold is the most frequent illness that humans experience. It is usually viral and consists of a stuffy and runny nose (clear to a little yellow) lasting for a few not-so-happy days. But at times the symptoms last longer. If green/yellow drainage and congestion are continuing for more than two weeks, then it could be a sinus infection and is more commonly bacterial. A trip to the pediatrician is a good idea and antibiotics are usually very helpful (as well as using lots of nasal saline - helps to decrease the duration and intensity of symptoms). If there is facial swelling along with the sinus infection then your child should definitely see a doctor (a CT scan is sometimes used to make sure nothing more serious is going on). If sinus infections are common (more than 4 in a year) and/or the nose if consistently stuffy in between the infections then visiting a pediatric otolaryngologist should be the next step. Besides looking for risk factors (allergies, exposure, immune system), strategies using medication, avoidance, and at times simple surgery (like an adenoidectomy) can be curative. In very rare cases sinus surgery is necessary in children. However this should not be a first line for children (unlike at times in adults).