She put her knitting to the side and stood up.

Literal

She [topic-は] knitting [object-を] side [at-に] placed [then-て] stood-up.

脇に置いて means 'placed aside' — 脇 ('side/armpit') is a near-synonym of 横 ('beside') in this context. The て-form links the two sequential actions: setting the knitting down, then standing up.