How does 一面向 break down in 她一面走着，一面向旁边张望着?
According to 现代汉语八百词, 一面……一面…… is used to indicate two or more actions are performed simultaneously. They are used before a verb. The first 一面 can sometimes be omitted.

Breaking it down from your sentence, you'll get:

她一面[Adv.] 走着[V]，一面[Adv.] 向旁边[Adv.] 张望着[V]

which means "As she walked, she looked sideways" (the same as you translated). Other examples:


  
  他们一面走，一面挥舞花环，一面欢呼。
  他（一面）用心地听着，一面记着笔记。
  


There's a side note, though. 一面……一面…… could also mean 一方面……一方面……, which means "on one side ..., on the other side ...". Usually 另 is added on the second 一面 on this construction, e.g:


  说明书土一面印的是中文，另一面印的是英文