One of the biggest organizing mistakes you can make is putting things away only to forget where you put them the next time you need them. Labeling helps avoid having to reorganize. (When you have all kinds of boxes, drawers and more to label, consider using an automated label maker to create labels that are more uniform and neater than handwritten ones.)
When organizing a nursery, label the boxes, drawers, etc. where clothes, diapers, bibs, bedsheets and everything else for baby are kept so no one has to dig through drawers and closets looking for what they need.
Label all formula and baby food in the refrigerator with a date.
Make a noteboard of important phone numbers (parents, doctor, emergency contacts) and notes (allergies, feeding schedule, medications, etc.).
If you use day care services, label bottles and personal items to make things easy on your day care provider and avoid mixups.
Every couple of months go through clothes and toys and discard or donate items that are too small or you don't use. If you plan to save baby items, store them in boxes labeled with the clothing size or appropriate age range.
For toddlers, you can use a picture on a label (below the words) to help them identify where their things are and where to return them during cleanup.