How do you dry up a babies nose?

Use a combination of a nose Syringe, and tissue. Putting a humidifier in the room will help with this process.

Find out the source of the runny nose, and eliminate it from the child, if it is smoke (which shouldn't be near the child anyways), dust, pet dander, etc... then remove it from around the child.

Sometimes it is best to let it run it's course, if it worries you too much check with your family pediatrician during their normal office hours.---Vegeta