Separation anxiety typically begins at around 6 months old to a year.  Here's what you can do to help you and your baby through this time period.
 
Create a secure attachment!
From the moment your baby is born respond immediately to her needs and cries.  Responding promptly will make her more confident and secure in your love and will help her to develop self soothing skills as time goes on.  This also helps with separation anxiety.  There is quite a bit of research showing that your baby's brain will develop the neural pathways necessary to soothe themselves if they are comforted when they cry and consistently have their needs met in short order.
 
Play peek-a-boo!
Playing peek a boo is not only a fun game which will make your baby laugh that adorable belly laugh, but teaches her that even though she doesn't see you, you still exist and will be back.  In clinical terms this is referred to as "object consistency". 
 
Fill your baby in on "the plan"!
Babies understand our words, and I have always let my little ones know in advance "the plan", which tends to make goodbye transitions a little easier.  Should the babysitter be coming that morning, for example, I will let her know this early on in the day.  Then at the time of the transition itself I say, "mommy is going out for a few hours and you will be playing with Lucia.  And, I'll be back."  At every goodbye transition I literally say these words, "I'll be back", so that it's consistent.  And, I definitely don't ever sneak out!  Similar to playing peek a boo, my babies have known that hearing those words means although I'm gone from their view, I still exist, and do in fact return.  I continue, with these same words at other important transitions as well, like during the first thirty days of preschool and kindergarten, when it's all new.