What tense is the sentence "He would go to finish the job?"
Other examples, "He would leave the store." "He would decide to help him."
Being a modal word, would doesn't really have a tense. Modal auxiliaries don't inflect. However, you can think of it as having a past tense, since would is also a past form of will. Having no tense doesn't preclude it from expressing it though. In your examples it could mean:
Depending on the context, but "would" can be the past tense of will.
Example (British Council):
I thought I would be late …… so I would have to take the train.