How do I stop my finished pencil picture from smudging?
Fixative spray will prevent most smudging. Use a permanent fixative for a finished work that you don't intend to rework at all. For an unfinished work, you can prevent smudging earlier layers by using a workable fixative. Always test on a small area first.
Hairspray is an easy, cheaper fixative alternative. This option is good for students and hobbyists, but is not archival quality and may affect an artwork negatively over time.
Archival art/photo sleeves are good for preventing smudging as a result of rubbing against other artwork in storage or during handling. They are flat, clear bags that come in many sizes and have a resealable flap to keep artwork from sliding out. 
Framing artwork behind glass will protect it from smudging even if you do not use any kind of fixative.