。
She pushed her way through people toward the train.
Literal
She [topic-は] train [possessive-の] direction [toward-へ] people [object-を] pushing-aside went.
押しのける (おしのける, 'to push aside') is a compound verb combining 押す ('to push') and のける ('to remove'). ~ていった uses the auxiliary ~ていく to mark motion away from the speaker — she pushed through and went off toward the train. 方へ (ほうへ) indicates general direction.